^ The umps did mess up one thing, though: They kicked Broxton out. The rule actually states that the pitcher would have to face one more batter. So Broxton should have stayed in the game.
Um, no.
In a case where a manager has made his first trip to the mound and then returns the second time to the mound in the same inning with the same pitcher in the game and the same batter at bat, after being warned by the umpire that he cannot return to the mound, the manager shall be removed from the game and the pitcher required to pitch to the batter until he is retired or gets on base. After the batter is retired, or becomes a base runner, then this pitcher must be removed from the game.
He wasn't warned not to return to the mound, so this doesn't apply and the pitcher is immediately removed.