It's entirely possible that the person who has gotten that far in the process literally cannot code Fizzbuzz. It's not an insult to be asked to do these things. It's a reality caused by the fact that some people can BS their way into anything, the hiring process at most companies is deeply flawed, and usually not the fault of the people you are talking to in the interview.
Obviously anyone who is that offended by this has never seen the other side of the equation where you've hired someone who turns out to be completely incompetent despite appearing to be very knowledgeable and smart in the interview, and now you've invested a whole lot of time and effort and money even if you are able to cut the person loose quickly. It happens. A lot. And it's often not because the hiring managers and other interviewers are idiots or otherwise failed to interview the candidate well.