Hit points are an abstraction. They're luck, they're skill with your weapon, ability to dodge, grace of the gods, whatever. You know that. I know that. The folks at my gaming group seem not to, however.
From the first edition AD&D Dungeon Master's Guide, page 61:
As has been detailed, hit points are not actually a measure of physical damage, by and large, as far as characters (and some other creatures as well) are concerned. Therefore, the location of hits and the type of damage caused are not germane to them. While this is not true with respect to most monsters, it is neither necessary nor particularly useful.
In the section on hit points on page 82, Gygax says,
It is quite unreasonable to assume that as a character gains levels of ability in his or her class that a corresponding gain in actual ability to sustain physical damage takes place. It is preposterous to state such an assumption, for if we are to assume that a man is killed by a sword thrust which does 4 hit points of damage, we must similarly assume that a hero could, on the average, withstand five such thrusts before being slain! Why then the increase in hit points? Because these reflect both the actual physical ability of the character to withstand damage -- as indicated by constitution bonuses -- and a commensurate increase in such areas as skill in combat and similar life-or-death situations, the "sixth sense" which warns the individual of some otherwise unforeseen events, sheer luck, and the fantastic provisions of magical protections and/or divine protection.
In a game where combat is common, there needs to be a way to tell when a particular character falls in combat. That doesn't mean that method has to reflect physical damage. In the example above, the DM didn't change the way the guy was fighting. The comment was more-or-less off-the-cuff, but it certainly reflects the beliefs of the other players: hit point damage is physical damage (to them). I've played with them long enough I find myself asking how beat-up an opponent looks, just like the others sometimes do. Pardon me whilst I mentally dopeslap myself. It's one of several things I hope to unlearn as I continue to explore old-school gaming, the world of player agency, rules-light play, and sandboxing.