I'm sure there exist jobs where its OK not to know that a mod operator exists, but none of mine were of those kind. I'm pretty sure my experience matches the majority by a pretty large margin.

> A fizzbuzz with fewer false-positive rejections might be something like "implement multiplication without using the multiplication operator".

While possibly a fair question, this is a whole order of magnitude more difficult than FizzBuzz. It requires more domain knowledge as well (lots of people have forgotten how to multiply).

> Allows the quality candidates lots of room to shine.

But this is precisely the opposite of FizzBuzz. The goal is to weed out horrible candidates, not identify great ones.