You are absolutely correct about that, and I am sure I have my wife's permission to say so!
For example, my wife had always been late. She did not apologize but will narrate all the circumstances that MADE her late.
I, on the other hand, would arrive at least 10 minutes early. Why? There's the off chance that she will arrive on time and will surely be very angry if I am not around. In which case I simply said, 'I'm sorry'.
But the beauty really, is that no matter what, things get sorted out and all is well again.
Fortunately, we never had major disagreements nor did something grievously wrong that a simple, i'm sorry, would not suffice.