That's a common trope I hear a lot, and of course sample size of one so take it with a grain of salt, but I've done tons of interviews with varying levels of engineers, and I've never seen any of the senior people fail FizzBuzz or anything like that (I never thought about testing Hello World), and most even do fine on the simpler data structures problems.

Maybe I've just gotten lucky, but I really haven't observed it. I've interviewed plenty of bad engineers, even senior level, but they usually knew the basics and had trouble with the lateral thinking required to solve the problem.