Originally Posted by totti

I think this is exactly the point. If you select a seat prior to check-in (with status of by paying for it) your seat is properly assigned in the system. If you check-in online but do not complete the process, your seat is assigned as long as no one else selects it. Only if you complete the check-in process the seat is properly assigned to you (but of course airline staff can still overwrite and issue a new BP at the gate).