Re: any singular noun or any plural noun?
I think the preference for the singular in this case, if there is one, is due to the fact that we're imagining one-to-one comparisons between the subject and a series of other boys.
If we imagine, as a thought experiment, a group of visiting boys -- for example, five members of an opposing chess team -- we could say...
They are stronger than any of our boys.
Is it certain we'd be imagining any one? I don't find that it is.
Also, if I were a basketball coach, and had to pick the starting line-up, couldn't I say: Any of the boys who have shown dedication will do. (Any five boys)."
So I am not convinced "any" has to be strictly singular in the affirmative. Which goes back to its original negative meaning similar to "zero, not, nought, null" -- which can't easily be classified either as singular or plural.