I think performance under pressure is a virtue. An important job is never going to be entirely free from stress - you want somebody reliable who will take that in their stride, you don't want someone who will buckle when things get difficult.
I'm all for in-person live collaborative problem solving, be it on a whiteboard or just a discussion. You see first-hand exactly what the person has in their memory, their problem solving techniques, how quickly they get things, their communication skills, and yes, their ability to work under pressure. If done correctly and collaboratively, you get a dry-run of a real design meeting and have some feeling of what it would be like to work with the person.