I tend to think that at least some regard for fairness is part of the common mental structures of humans

I agree with this in a sense, but only in a sense. It seems to me that every culture has a slightly different idea of what 'fairness' means, to the point where the word itself doesn't really translate from one language to another. (Or perhaps I'm thinking of 'justice', which still seems similar enough to count.) The tendency to have something-like-fairness seems pretty universal, though, even if the specific concepts involved aren't.