The whole point of fizzbuzz is to filter for people that can just solve a tiny problem in a reasonably short time-- that's it. Most interviewers will even give some slack if the person has to look up the modulo operator or even do with out it.

If someone can't do it at all there's some kind of serious issue with the way they're approaching the problem, or perhaps they're just not capable of doing it.

But another common way for people to fail or at least get red-flagged is to over-think it and come up with a turgid solution-- like using lambda calculus!

Simple problem. Simple solution. Nothing fancy. Going against that is asking for failure.