I understand business meeting times. I understand showing up to class on time. I don't understand times for meeting up for pleasure (drinks, dinner, dates). I just don't.
First situation was someone was supposed to come in for an interview but didn't show and then emailed 15 minutes after the scheduled start time saying she had a family emergency and got flustered on the way to the office and decided she needed to take care of other things instead of come to the interview. We have no idea what happened, but the other members of my team immediately concluded that she had blown her chance and we wouldn't be asking her back in because she wasn't "professional".
The second time was arguing about that situation where if I had meetings and a family emergency came up the last thing on my mind would be canceling the meetings when the other people in the conversation said the first thing they would do is cancel the meetings.
It's an interesting juxtaposition to be sure.
You are really being very disdainful of the (hypothetical) late person. I find that is a typical American attitude. Even in this completely theoretical discussion, you are assuming the person is late for a reason you find frivolous instead of being a receptive, empathetic human who knows that things don't always happen as planned.