FizzBuzz is not some arcane algorithm. You don't need to study it.
It's literally writing a loop, testing equality, and printing some output. I don't know how you could program professionally and not be able to solve FizzBuzz.
This is the same for a lot of the basic algorithms we learnt and forgot.
This, to me is the big caveat. Just as there are a lot of people who are horrible at solving stuff they should easily be able to, I've conversely seen so many horrible interviewers that under-specify the problems they ask about because they assume people should understand algorithms that would make it easier to understand, or just assume people will infer things most people wouldn't.
"Take these two variables, derpyOne and derpyTwo, and swap their values"
same here - almost 20 years of dev, last time I needed to implement basic cs algorithms were in college and grad school classes (and some idiotic corporate interviews where preferred way of coding is apparently using a white board).
basic knowledge of fizbuzz, dfs, bfs, quicksort, and similar things of course is needed - however asking developers actually implement them in front of you is pointless, at least as far as job performance goes.