The reason why I've never considered hit point loss to be "real" damage or injury is because of the loss of versimilitude I see between D&D combat and "real" combat if I did.
In actually swordfighting... especially between highly armored individuals, you usually don't see actual real injury occur until one of them manages a killing blow. Instead, you see two guys getting bruised, getting tired, getting their bells rung, slowing down, perhaps get some small cuts across the face or arm... until finally someone manages to get their weapon past their opponent's defenses and cuts off a limb, or guts the other guy in the stomach or face. But once that happens, the fight is over.
Now for the guy who wins... he usually isn't massively injured, because if he was, he wouldn't have been able to continue fighting. His guard would have dropped, and he would have been the one to have received the killing blow (or the 'took such a catastrophic injury that he ain't getting up any time soon, if ever' blow.) Instead, he takes off his helmet, he regains his breath, he drinks some water, he maybe bandages some superficial wounds, and he then gets ready to continue on to the next battle. He never was actually hurt.