I've never really felt it was that different, but for the sake of discussion, how would you simulate the non-social variety of stress in a hiring situation?
This does put on some pressure - there is a deadline, after all - but people who are shy but confident in their coding abilities may be less anxious. This would also solve the common "but I wouldn't code without an IDE/Google/Wikipedia" complaint.
I've had phone interviews where I've been asked to solve a logic puzzle with pen/paper while explaining my approach. Solving a problem you've never thought about while being put on the spot turns out to be incredibly difficult. These sorts of problems require deep concentration and quiet yet it tends to be awkward to have silence between strangers. The situation really inhibits serious problem solving.