Ask a firefighter who rushes into burning buildings for a living to give a public speech in front of a large crowd of people in a non-burning building. Which is more stressful? For the firefighter, it may be the latter. Fighting fires is what they train for, what they're experienced with, whereas giving speeches is not.

A lot of people, no matter the profession—firefighter, programmer, etc.—have a great fear of public speaking. Likewise, a lot of people, no matter the profession, also have a great fear of job interviews, especially the crazy audition-style interviews of programmers. It's simply human nature, with little bearing on job performance in general. We shouldn't be giving auditions to people who aren't stage performers. Personally, I never work with someone watching me, nor do I ever have some specific narrow time limit on my work in the range of 15 minutes or so.