Fizzbuzz may seem natural to people with an inclination for numbers or formal schooling that forcibly crams lots of math you'll never use down your throat, but some people haven't been taught about modulus operations and some people may not be very good at division and would take a while to try to reinvent mod. Neither of those things are necessarily really big problems if that person is going to be writing business logic (though you might want to have someone check any code they write which involves money).

The idea of "fizzbuzz" is to show basic understanding of language control structures and flow. Better, more universal tests that actually use language constructs that are encountered in daily operation could definitely be devised to demonstrate the same fundamental concepts.