I think they should be set by the administrator, so it's consistent. It would be very confusing if each user is identified differently.
There's an issue with username vs. screen_name, which is that screen_name is unique site-wide, whereas usernames are only unique per authenticating authority, because we cannot control these. So there might be two users with the same username, if you have multiple authorities configured.
But right, for single-authority-sites, they'd be equivalent.
/Lars
