You certainly have a point. But those whiteboard interviews people complain about are usually a bit harder than just solving FizzBuzz.
I've seen a respected engineer that I worked with for years, be told by an outsider that he was incompetent because he couldn't fizzbuzz an interview. Yet, they had no problem acquiring the project he designed and wrote.
So yeah.
Why couldn't he do fizzbuzz?
"Why couldn't he do fizzbuzz with someone else watching his every move while he wrote on a blackboard with no interpreter to test his solution or catch his mistakes?" seems like the better question.
You're assuming quite a lot here. Was he not able to write flawless code without syntax errors, or did he struggle with the core idea of FizzBuzz?