Corresponding to the umpire-as-instrument idea is External Realism. According to External Realism, there are umpiring-independent facts of the game — balls are really fair or foul, runners are either safe or out — and the questions we face are merely epistemological, how best to determine the facts, how to find out.
Corresponding to the umpire-as-player idea is Internal Anti-Realism. According to Internal Anti-Realism, umpires don’t call them as they see them; umpires, through their calls, make it the case that a pitch is a strike or a ball, a runner safe or out. There are no umpire-independent facts in baseball.