It is very common for people to be able to come up with the right answer without knowing precisely why it is the right answer or to articulate why that is the right answer. The distinction you make between being able to "generalized" and being able to "abstract" sounds a lot like being able to do something unconsciously without being able to do so consciously and rationally.
(The process of "abstraction" that you describe sounds very much like what is often called "inductive reasoning". Many dictionaries define inductive reasoning as the derivation of general principles from specific observations.)
When a policeman arrests or searches someone but can't articulate the reason he did so, and it turns out that the person actually was guilty, we call that in the law a "hunch" (if the policeman can articulate a reason it is "probable cause" instead). But, a hunch is usually not just dumb luck and instead is actually a situation where the policeman arrested or searched someone and was correct that there was a reason to do so based on observational evidence and the policeman was simply too inarticulate to explain why.
Similarly, the popular book "The Gift of Fear" articulates the concept more generally that "gut instinct" can often more accurately diagnose risk to your person than conscious reasoning processes.
At a neuroscientific level, this basically arises because the older limbic system in the brain (sometimes called the mammal brain) has specialized sub-systems devoted to threat analysis and honed by natural selection, that the more generalist and younger cortex unique to higher primates, does not. In contrast, different parts of the cortex are involved in different subparts of inductive reasoning.
It also bears some resemblance to the notion of blindsight, which "is the ability of people who are cortically blind due to lesions in their striate cortex, also known as primary visual cortex or V1, to respond to visual stimuli that they do not consciously see."
Another example is a rule of English grammar concerning adjective order that almost no native speakers of English are aware of, that is not found in any common school grammar books, that native speakers nonetheless slavishly follow without knowing that they are doing it. Native speakers will recognize that a sentence that does not follow this order is off, without being able to articulate why this is so. English as a second language learners, meanwhile, must be taught the rule.
In the Star Wars universe, people who are "strong in the Force" can similarly act with superhuman awareness and precision by letting the Force guide their bodies subconsciously rather than relying on their conscious observations and rational conscious thought processes.
In short, this very much makes sense and could easily flow from a brain structure in which brain structures in the subconscious mind are capable of categorizing or generalizing in some particular domain (ideally one with a great deal of selective fitness value) and another part of the brain engaged in abstraction and articulates the basis for the generalization. If the latter structure is absent or ill developed, then the phenomena you describe would arise.
