> I assume you've never tested the negative hypothesis and gone ahead and hired somebody who couldn't program fizzbuzz to validate your assumption

A former employer of mine inadvertently did! He wasn't asked to complete FizzBuzz, but I am confident he couldn't answer it as I worked on the same team as him. He was a very charismatic individual who always "needed help" from team mates on all tasks, no matter how small. He managed to collect a salary for 6 months. Some time after he was let go, the police called my employer enquiring after him, and we learned he was a conman with outstanding arrest warrants with no prior SWE experience at all. The name we all knew him by was just one of many aliases.

You're right. When interviewing for a team that writes mostly in C and assembly (assembly for various different ISAs), we're not going to hire someone who claims to know C and fumbles through some basic problems and can't reason about hardware in the slightest.