I believe as umpires we SHOULD care how a game is scored. Official scoring rules are just as much a part of the game as playing rules are. I think we should be as informed as possible about official scoring rules just in case we are ever asked about them. In the leagues I umpire, whenever there's an interference call (or something else that's a little bit unusual) at the end of the inning I'll let the home team's scorekeeper know who ought to be credited with the putout. It lets them know that you care about the game. It can't hurt; it's good
PR work, if nothing else.