The controlling issue usually involves each airlines' internal policies and union rules, rather than government agency oversight. You have to be qualified as captain, but that's no problem as instructor positions give the FO the fourth stripe he needs. The problem comes when he wants to line fly and the intervening union rules. Does he fly as FO or Captain? Of course, it's different everywhere.
Some unions implement rules like the instructor (with low seniority), can instruct, but is prevented from checking until his seniority reaches a certain level.