Well, I'd have to say that the coach is being ridiculous, however ...
I like what Marie C said. The lesson you can teach your son in this case is that each place and each teacher/coach/activity leader is going to have his/her own set of rules, and these rules must be followed and respected. Granted as adults we might come across a rule that we do need to challenge, but that is between adults.
One of my teachers in 6th grade told us on day 1 all the work we would need to complete by the end of the 2nd quarter - kind of like giving us a college syllabus. It freaked me out!!! My dad (who has a PhD in Psychology) talked to her about this and suggested that maybe that was not a great way to present it to the class. She went on and on about what psychologists say and why she was right. He finally got fed up and said, "Lady, I've forgotten more about psychology than you've ever learned!" But he didn't tell me this until I was in my 20's. When he talked to me, he backed her up.
I do think the coach is being ridiculous, but I also think you need to accept her rules and back her up. Teach your son that he needs to respect her and her rules. It's a really important lesson for him to learn.