I think you're misunderstanding what folks are saying. How the scheduling is handled differs in every state. And in many states, it differs in every county within the state. In Pennsylvania, it's an absolute insane system. There is not a state-wide scheduling mechanism. Some counties in PA allow you to register for a shot in their county. However, the county health department doesn't control all of the shots issued in the county. Many of them are in pharmacies or in hospitals that made agreements with the federal government. So in those situations, you register with the county health department, but you also go out and register with the hospitals and pharmacies in your area. None of these are appointments -- you are just getting on multiple lists, and waiting around for the first one that contacts you.
Once you receive a shot, it is considerate (as
@The Spin Meister indicated) to go back and un-register at the other locations. However, even if you don't do so, it's not as though you're being selfish, as all that would happen would be those other sites would either e-mail you or call you to say that they can schedule you for an appointment, and you tell them that you've already received a shot elsewhere.