Sometimes, I tend to overthink politeness.
For example, we have an elevator at work before the exit door. If I am in the elevator with someone, I would want to hold the door open for them but that means barging out the elevator first to be able to do that to get to the door first.
But if I usher them out the elevator first with an "after you" and wave of my hand, it means they have to hold the door open for me. So am I being rude or not?
The story above reminded me of the fear men sometimes have of PC rules. If a guy held the door open for you, would that make him a sexist and demean your "power"? So, better off he treat women exactly the same as men with zero differences. If he is impolite with guys, then he naturally should be bad with women, also. Otherwise he is a sexist.
So, in a very twisted way, the fact he was rude to you by not holding open the door may mean he respects you enough not to demean you by treating you differently.
Also, I think politeness is dependent upon the current situation at hand. Social rules are somewhat fluid. It is perfectly acceptable to wear a bikini at a beach. But now imagine wearing one at a fancy dinner party. Different situation, so the rules change.
Apparently it is considered acceptable (not by me) for sportspeople to spit on the pitch they are playing on during a sporting event. But now imagine someone doing the same thing at work or home.
Social rules are quite fascinating from an anthropology standpoint. Why do people do what they do? And why do we imbue these small rituals with such emotion?
The OP happens in real life everyday. I have had people come up to me and just start "Where is the.... How do I get to the..." without the introductory "Hi, I was wondering if you could help me?". Heck, even the "Hi" would be good enough.
But all that is just a social dance that we do. So many rules in society. Many of them quite silly.