Green blood can be seen somewhat through the skin
That doesn't mean they HAVE green blood, however. I have red blood when you cut me open, but the veins you CAN see under my pale-as-heck skin--those are blue, NOT red.
Contrary to popular belief, blood is always red, even if it hasn't been oxygenated.
So why can blue blood be somewhat seen through the skin on pale people?
It's an optical illusion.
Sometimes blood can look blue through our skin. Maybe you've heard that blood is blue in our veins because when headed back to the lungs, it lacks oxygen. But this is wrong; human blood is never blue. The bluish color of veins is only an optical illusion. Blue light does not penetrate as far into tissue as red light. If the blood vessel is sufficiently deep, your eyes see more blue than red reflected light due to the blood's partial absorption of red wavelengths. SOURCE
Stuff that's really close to the surface in the capillaries still look red (which is why lips are a ruddy color).
My point here is that you can have the effect of them looking green, or their blood looking green when it is inside them without their blood actually BEING green. All you have to do is add yellow to their skin structure. Not a pigment, the actual structure. And even then, they STILL might have pinkish "lips" or whatever.
So they might look unusual and colloquially they might refer to their green blood (which if they are herbivores makes sense), kind of like how we talk about blue bloods. An outsider might actually believe that they have green blood inside, because it's talked about and they have a "green cast" (ie. deep vessels that can be easily seen with more frequency than human vessels through yellowish skin) when in truth, they are just as red-blooded as we are.
Those who are suggesting a higher oxygen level on your planet to allow for the blood to actually be green, there are theoretical models for that They use OUR planet as the model so YMMV. Basically more oxygen = less rain. So you're going to have to come up with another reason for it, or rebuild the atmosphere in a different way.
Planet of the ?
While we are on the subject--an entire planet with one atmospheric condition is a big trope. And for a planet that sustains life on a complex level? Very strange indeed. Humans are versatile, but where we came from informs what we are like--we walk because we needed to see predators in the grass. Your folks might prefer gloom and wet to sunshine and settle in places that have that, but the whole planet being one particular way, is a stretch.
I think this stack exchange link will be useful to you: Why does my species tock like it ticks?