Not a good move to confront the coach after the game. Other parents probably saw this and coaches don't like to be approached after a game and he will more than likely carry this with him.
Your son should have been honest about the injury to the shoulder much sooner. I know, I know, he did not want to disappoint or feel like he was being a wimp. No excuse....he needs to learn from this and take his lumps from the coach...no matter what the AD from the other school said. That was a bit irresponsible for an A.D. to say that. He probably was just trying to side with you to give you comfort knowing full well the coach was well within his bounds with players the age of your son.
I yelled at my center fielder (age 11) for taking a seat in center field. He took a seat while the pitcher was actually pitching to the batter. He was the other coaches son (who was on vacation). I stopped the game and called him out in front of everyone. He was 11 and fully capable of knowing he was taking advantage of the situation. I told him it can't happen again. Do parents like that? Heck no! they hate to see it with their kid or another.