Earlier quoted context omitted.
Being a professional programmer is not an entirely stress-free job. Often, time matters and you have to think on your feet. That's why I think rejecting a programmer for losing their core competencies like problem solving, i.e. freezing, under a medium amount of pressure is valid.
The stressful situations tend to be things like "We just broke the production database, we need to figure out how to recover the data ASAP"... not "We need a new algorithm in FIVE MINUTES!"
I know you did not mean it this way, but in some ways that's even worse. If that type of thing were routine enough to merit asking every interviewee that question, I would seriously reconsider working there.