Brendon was only sure he broke it when he heard it snap. No one heard it snap other than Brendan or Tommy. Yes, if the ref knew about it, he should have ended the fight. This is why it was set up in the first fight that Tommy knocked out a seasoned fighter with one punch from one arm in seconds, to give the audience the idea that Brendan had the advantage but Tommy, even with one arm, could still possibly win even to the last round.
IMHO, part of the ending that transcended it from a typical sports film was someone finally acknowledging, for the first time, Tommy's pain and that he had been abandoned his whole life. ( His dad was a drunk, Brendan left him for a girl, his mother died, the Marines friendly fired and wiped out his whole unit) When Brendan tells him it's ok and to let go, he's not talking about the fight, he's talking about Tommy's pain. He doesn't truly understand Tommy's pain until he sees him half crippled in the ring but won't give up and he sees his father is not there for Tommy and Tommy calls out "Dad?" at the end of the third round.
Brendan believed his father loved Tommy more because he trained him as a child and focused on him, that plus the alcoholism split their family, this is what drives Brendan to want to fight rather than lose his "home" He never had stability growing up and he never wanted to do that to his own children. This is why he's a teacher, to help other people's children. This is where I think the plot has a sticking point that will hang up some of the audience, most people would think Brendan should just take the bankruptcy and leave his house rather than risk his life.
What Brendan had to "let go" is the wall that blinded him to the reality that his brother needed him, and because he was so concerned with not being like his father and winning his father's approval, that he neglected Tommy. This is why at the end, Brendan is not finally vindicated that he "won" in the eyes of his father, but that he simply told Tommy he loved him and walked him out of the ring. When Tommy finally "taps out", it isn't so much his acceptance of the loss of the match but his acceptance that it's ok to let go of that rage inside of him, that he isn't alone anymore. The issue with the father at the end was that he finally accepted that he couldn't be forgiven for what he had done, that he couldn't make up the past, that his sons wanted nothing to do with him, but with each other, without him, they had a chance to not be like him.
What I love about the movie is it allows Tommy and Brendan to only be the kind of men that they chose to be for themselves. Both men are driven by their sense of duty, and not what they feel. This is why they resent their father more for his apologies, they see right through his selfish core, than his abandonment of them. It's why in every other fight, they would simply not surrender, they never saw it as an option nor a choice. The theme of "Moby ____" was that every man has a "white whale", every man has an internal battle he must overcome, a personal demon, to find peace. What's interesting about the film is all three won, but all three also lost. But it wasn't about their winning or losing, it was that they could finally accept it.
