Technically yes, but today no.
We know barely how a humans brain work and therefore we know information is beeing stored using electric impulses. These electric impulses can be triggerd from outside as well, but the point is, that (today) we just don't know exactly enough, which points to trigger to get a specific information saved, and also we (today) can not exactly know, what information the brain is actually processing, when we see, where the information (voltage) flows.
We already know, which areas do which things, but that is definitifely not enough.
Its like a computer. You know the brain is the RAM and you also know, that something between 0x0000001 and 0x0000007 to something between 0x00006F0 and0x000B71A is somehow connencted to language and speaking and you even know some other vague areas and a part of what they do.
BUT even if you capture "ahh this does language" you don't know "this is working on the word "pineapple" at the moment"
Saving information to a RAM/brain where you already know that much and nothing more ist just not possible.
Also Reverse Engineering is somewhat difficult as we are talking about a living brain inside a human. You can not rewire this for try and error, because of moral aspects in as far as I know every country of the world. But even if someone says "hey, take my brain and do what you want even if i'm still living" this doesn't help you that much as you have to exactly know, which information in this RAM does what and how to access it.
Also every RAM can be accessed the same way and can be called the same way (mostly) as you have standards like DDR2 and the given size of the RAM (eg 2 GB) and input voltage and so on, but a brain doesn't follow some ISOsor even vague standards and therefore every brain is diffrent. Also there are tumors etc, so even if you could access a brain it, the way of how to do that would be different from human to human.
Also the brain is not entirely RAM and it is not entirely a processor. It works like a mixture of both of them. I'm not very into this, so ask a doctor for details, but a brain does (in my oppinion) not have a processing unit and a saving unit, but both things can be done somehow simultaneously from different regions in the brain. Given that you can not easily save information as you have to follow the brains "workflow" as the brain needs to get input to a specific time at a specific location based on what else is processed at this time and shot before as this most probably affects the way the brain stores this information correctly or not.
So putting together all this: Yes, one can possibly do this in the future, but nowadays this is somewhat impossible due to the reasons above.
Also if you successfully manage to enter some information into the brain (let's say 0011101100001011 at some place) you can definitifely not know, how exaclty this affects the brain. Sure if you reversed the brain enough and you know that memory address of the word "banana" and you manage to change it to "apple" this does not mean the person is from now on saying apple to every banana it sees for as I said above the brain is also a processor and not just memory, so maybe this throws an exception (apoplexy in worst case), because the brain expected a different word or abstract datatype.
-> good point. Abstract datatypes - those are things the brain uses to store information in and it does this, because it defined those datatypes based on its experience/knowledge influenced by the very personal perception, which means that every human saves his/her information in a slightly or heavily different way.
We know the brains error handling in some aspects. If we stay outside in the cold for a few days for example the brain may respond in shaking your body and felling pain or we know that getting a virus may lead to overheat the head, but we don't know yet, what the brain does (to us) if we manipulate thinking.
Back to the areas: Even if we know, which areas are responsible for doing things like speech, listening, seeing etc. we dont know, whether this covers the brains ability to save/store information or whether this is processing those information. So we know a brain acts as RAM and processor and we know some areas and their job, but we can't tell if the job is of the type RAM or procesor.
An additional thought on this: If humans think about bungling things in our brains - what do you expect from an AI?
I think an AI would try to do similar things if it is bored. Before the AI does this you don't know if is good or not. Good means for us humans. The same applies to your question. We don't know what humans will do with the ability to change other humans (and their own) thoughts. It could be either good or bad. Using this feature beeing bad is probably more likely to happen as most humans are assholes and they would try to use this opportunity for whatever, but that is not part of the answer.
Coming back to your question:
it's up to the receiving human to verify it
I disagree. The verification of information stored in the brain does also have to be stored. Think about
An apple can be eaten, which you KNOW is true and
an apple is the same as a banana, which you KNOW is false and an information
an apple is Gk(g5sP, wich you cant answer. Then there is
an apple is red, wich you don't KNOW - you have to say "possible". But then there are information like "cousin Anna is 42 Years old", wich you probably just think might be correct as you didn't saw her for a few years. So if you just enter raandom information into a brain I would expect the brain to say something like "nope, that is false" or "don't know - might be fake news".
Think about it: If you know, that in the past you never heared the word "Gwabbrügtz", but now you know it is a city with 81234 inmates and [...], but you cant combine this with experience, then you'll most likely say, that this information is not true as it might be a part of a dream last night you can't remember. So if you place information into the brain you have to ensure yourself the brain is 1. thinking the new information is true and 2. dealing with the new information in a healthy and good way.
So no, it's not on the person to decide, whether the information in the brain is true - this is always determined previously by experience. You dont decide every time your asked, whether an appöle equals a banana -> you know this for sure to be false. So the knowledge whether this information is true is already in your brain. Therefore if someone manipulates the brain with information the validity of this information mus be transmitted as well as otherwise the brain would never think the new information is true.
Matrix style "I know Kung-Fu" learning
If it is already possible to make a brain believe things you entered into it, then there is absolutely no problem to apply this for muscle navigation as well.
I wrote about those abstract datatypes and that every brain has to be accessed different, so the information, what to do with muscles is not one of the hard problems. It in fact should be really easy in caomparison to what it needs to successfully change a single bit on purpose (with knowing previously what this will change).
Also: Nowadays it is possible to make a brain do things with muscles. This has beend tested on animals (mice) and it works, but i dn'ß think it would be that easy with a human brain (without causing damage in any way / while this feature is under development)
I called the brains memory RAM as all unsaved changes will be lost if it is shut down. Nevertheless this can be changed. If one manages to change the brains memorys content the brains memory capacity can be extended as well so you can for example connect somehow the brain with some SSDs to make the brain store its information in there. Also this could result in "sharing memories" in a different manner we usually do. Instead of using speech the brains memories could be saved onto physical devices such as SSDs. To do this you have to implement sort of a driver to let the brain have read/write acces to this storage and then you can define how the information have to be saved on this external storage.
This would make it easy to build a knowledge database for every (connected) human to make use of. Also you could stream information from this storage or from another brain directly into a "new sense" (a few of them we know as touch, smell, taste etc.). This would allow direct communication between two brains, so you could for example use the left arm of another person as you do it with your existing two ones. To enable this feature you have to write a driver for this into the target brain. This driver should be different from human to human, but the data inside the storage can have a standardisized format to reuse this fpr other brains.
To take those thoughts a bit further:
If we think Matrix style leaarning a huge amount of things in a few seconds this could be possible - or not, because if you hear someone speaking you're fine, but if you hear his/her voice 20 times faster it gets confusing and you will most likely dont get all the information. I think it should be worth a thought if that could apply on the brain as well. As the brain is not just RAM, but also a processor it could be happening, that entering information triggers some kind of thinking (which is very likely) at least in the way of "what information I already have can I connect this with?" as we usually try to do this with normal learned things. So as a processor we have to ensure the brain does not overheat on the amount of things it is confronted with, so maybe it would be very slow to enter information and maybe not. I don't know and I don't think there is evidence for any answer to this as there is no such experience yet. It's just very likely, that in addition to the other circumstances the speeed will also be kind of bad for things humans would like to do.
Also it would be difficult to get a save place to enter information as the brain can't be shut down without having exceptions thrown a lot after a reboot. Save place means, that the brain does not try to use the involved neurons at the same time as we modify them, because that would probably cause the brain to do some weired things. So you should make the area you want to edit not available for the brain for the time youre modifying information, which could be done by cuttin some synapses and "rewire" them after modification. To make the brain work properly in the meantime you could mak an exact copy of the area to modify, build a temporary storage, which the brain accesses as it was the space it would normally be and then you have to "rewire" the synapses. This is just an optional step, but for a good working solution this is a must-have.
So if you want to know, whether such a thing can be done SAFELY the answer will be no for a few hundred years.
Nevertheless it is possible, but it will take very long to be able to avoid errors and it will be very expensive as well and at least the beta will still cause some mental deseases and deaths.
To sum it up:
Yes. To change a brains memory or adding new information should be technically be possible (magnetic stimulation or you're really using wires^^) but given the problems I mentioned above it is much too hard to do. Especially that what programmers understand as "abstract datatypes" may be a real hard problem for people trying to manipulate brains as their declarations/definitions will (most likely) vary from human to human significantly.
*I didn't read the other answers entirely before posting, so maybe there are some acpects already coverd by some other answers