I would not want to "show up" an umpire. I am not talking about coming onto the field and waving the book around to make a point. That is why I added the part about coming over to the dugout. No one in the stadium needs to know what is going on. For all they know you are fixing a broken piece of your gear.
I just wanted to know how important it was to umpires to make sure the ruling on the field was correct. The consensus from this thread is “not so much”.
Well what about this scenario? I am sure all of you would never dream of such. Earlier this year my school was hosting a tournament. My team was not playing, but something came up on the field and the umpires and coaches were discussing what the ruling should be. I was close by and one of the umpires came over and asked if I had a rule book because he wanted to make sure he got this right. I did, and after a quick glance at the book the right decision was made and the game went on without a hitch. No one in the stadium thought less of the two umpires because they checked the rule. In fact it raised my view of this umpire and I have requested him for our play-off games this week.