Note that the FizzBuzz Test requires at least some simple number theory thinking. Yes, some small children understand it, but most people with standard schooling are not comfortable with the ideas of multiples, common factors, modular arithmetic, etc.
I only point this out because 199 out of 200 should make us question ourselves about the test. I’ll accept that 90% of so-called programmers are “low functioning” but not 99.5%.
Is this FizzBuzz-style number theory knowledge required for programming? No. Does it help? Yes, a lot. I find applied mathematical knowledge to be a better indicator of quality, efficient, expandable programming than a checklist of fad languages and environments.
But, still, watch out for hiring only super-nerds or your product will be super clever but unusable by “normal” people. A little bit of variety of backgrounds helps.