In the example you gave the I’m sorry isn’t a real apology, it is social shorthand for ‘I didn’t mean ’ whatever. In this case that the unwanted contact occurred. You do understand that today there are people who will attack you verbally or physically for this kind of situation, whether it is brushing an arm in passing or cutting another driver off. An automatic ‘I’m sorry’ can mean ‘No problem’.
I find I say ‘I’m sorry’ when someone says something I didn’t hear. There are physical cues that go along with it but basically means ‘I didn’t get that, please repeat’ not that I have done something wrong,
Then you have the ‘I’m sorry’ that really means the opposite. We hear this a lot from politicians and other public people. They will say or do something stupid and say ‘I’m sorry if you were offended’ implying that it is not their stupidity but our hyper-sensitivity that is at fault
We need the social shorthand phrases to keep the wheels of human interaction greased. How would you like it if common courtesy required a full and heartfelt apology with an explanation and promise to be more careful in the future? Or if there was never a recognition of a faux pas?