On the contrary, I think this is a huge red flag. Just go along with the interviewer, maybe highlight that this is typically and entry-level problem, but solve it. You really don't want to hire someone who not only can't solve fizzbuzz, but also refuses to hear about it and complain that it's 'beneath them' (what a annoying attitude!).
Depends. It could be an indication that there's been a miscommunication and the interview is for a much more junior position than expected, so I would expect a more senior person to push back. Fizzbuzz tests "can this person program at all?" For a more senior position, best to start with something harder and more job-related; back off to fizzbuzz if the interviewee can't do the hard stuff.
FizzBuzz typically gets raised eyebrows from folks who never had to do it because they assume there's a trick somewhere. It can't just be a one-liner they assume.
Imagine you're a senior developer with over 10 years experience. You're happily employed and make good money. You're contacted by a recruiter for an interview. Perhaps the company even uses some software you wrote.
"Ok this problem is called fizzbuzz. We just need to see if you can really code."
It sounds like the situation was of course different, but situations like above have happened.
