The number of people who find fizzbuzz hard makes me wonder if there's something that I find straightforward to understand in it that's actually harder than it appears, which makes me avoid it as an interview question. I want to find good devs, not good Fizzbuzz authors.
Yes. Fizzbuzz is redundant, perhaps by design. If you start thinking to optimize the redundancy away, like “why do I need to divide by 15, if I am already dividing by 3 and 5”, you spend some precious 30 seconds thinking, and look exactly like an idiot who doesn’t know how to program at all.
The secret there is to vocalise your thought process. Interview puzzles are as much about assessing the candidate's critical thinking skills as they are a filter for programming knowledge.