Now, I do my level best to make interviews unstressful. I don't think a stressed candidate is going to do their best, or be their best. They're going to be second-guessing their answers.
That's the point of war stories. Every experienced candidate has them. We've all done memorable things in our career, both good and bad. If it sticks with you, the details aren't what matter.
edit: This goes both ways. I expect the war stories to be an exchange, a patter. They should be learning about me and my co-interviewers as well. And, as someone who gets interviewed, if I feel the interview is completely one-sided and not revealing anything about potential colleagues and the working environment, I'm going to hesitate.