It is in Rome. Vatican being sovereign nation is relativelly modern invention (1929), for the longest time, it was simply a part of Rome. It's basically a glorified borough. If let's say Manhattan became independent, would it suddenly stop being a part of New York? I guess you could say that, I wouldn't.
it would be nice if you could change the office clue and answer slightly - the UK show is set in Slough so would still be an S and fit nicely into this quiz as an alternative answer (if you remove the bit specifying Pennsylvania)
Consider the context, the answer isn't in isolation - look at the question, "Sherwood" is perfectly fine as an answer when taking everything into consideration.
Personally I think it was great that Question master tweaked the question (which was US-specific) to acknowledge the original series, given both their settings start with S.
Although I tried to guess it, I was just sure it was St Paul's. But that's every OTHER cathedral in the world.