I think that's a conditioning thing, not an inborn response in either. Anyone can be socially anxious. It's just that 'NTs' are better at socializing in the expected ways, and thus do not get chided nearly as much for anything they do.
When I observe people, I notice almost everyone seems anxious when they're socializing with people they don't know, especially in close quarters or large parties. Anxiety is a normal response for any social animal, since there's always a battle of finding position, especially in new situations.
I'm less anxious talking with people I'll never see again than I am with people I have to be around frequently, since there is far less emphasis on status. I'm usually the first to start a conversation on a bus or plane, but it's hard for me to get anything started at work. And that's not uncommon, as far as I know.