Not likely that the ump is a Braves fan. More likely he flat missed the call, and, being an umpire, cannot admit he might have made a mistake.
Davey's rant serves to keep him alert.
It's one thing to have a drunken wacko like poor old Billy Martin argue a call. Or to have Ozzie G throwing a tantrum. It says a lot to the entire crew when Davey Johnson argues, and, most likely, the other umpires say after the game, "Hey, you missed that badly".