Saying "I am sorry" does not necessarily make everything right, but it does take courage to utter those words. I have known many people who are unwilling to say those words, no matter what; they would rather die than utter them, and they have done so. In my explorations of that phrase, I have come to the conclusion that even when delivered in a sarcastic tone, they have intrinsic power, which is then shifted to the recipient. For that reason, I no longer debate and analyze that phrase, whether delivered to me, to someone else, written, spoken in film, etc. In whatever context they are expressed, I accept them instead of blocking them.
I question whether the utterance of that phrase was ever intended to make everything right. Instead it is a phrase which opens the gate to the magical, wonderful path of forgiveness.