Not once in my career had I had to fix a problem in an hour, let alone 10 minutes.
I have had senior people get mad at me when I couldn't give an answer during a meeting - that's the closest to an interview type scenario where you need the answer now. But even then, I did not stress that I'd lose my job, which is similar to the stress the candidate is facing.
Yeah, but if so it's usually of the form of "oh shit, forgot to chmod this little bash wrapper".
To the extent that it's of the form of "Solve this cute little dynamic programming problem I heard about from some company where everyone is like, gosh, oh so smart! In like, the next 5 minutes, k?" -- well, basically never.
It's like interviewing a doctor who will be someone's primary care physician. Give him/her a set of symptoms, and fail him if he doesn't diagnose it inside of 10 minutes. And then justify it with the expectations in surgery or ER.