Warlord as an HP proxy war.
Allow me to see if I can sum up the issue without acrimony.
First, I should clarify that HP debates predate 4e. In point of fact they pre-date the Internet, and ARPA-net. Gary Gygax wrote a "clarification" of the concept way back in AD&D that muddied up the waters and people have been arguing about it ever since. 4e simply dragged the issue out in the open and made a declarative stance, which pissed off every one on the other side of the debate.
So. There are (roughly) two schools of thought on HP. One is crudely expressed as "meat points", where someone with a lot of HP simply is impossibly tough. The other side views HP as nebulous in form, combining morale, luck, fatigue and plot armour. In the second view "hits" which deal damage may not involve injury, or even contact, but still drain the character of a resource labled HP for convenience, it's only the final hit that drops a character that actually hurts. Maybe.
Part of the problem is that HP are not, and never have been a wound or injury tracking mechanism. When you get hit by a sword for 5 points of damage, you don't know where you were hit. You don't know if it was a cut or a bruise (strike failed to penetrate armour or you were struck with the flat of the blade.) And it doesn't matter. A hit in the leg doesn't slow down your movement. A hit in the arm doesn't reduce your manual skills. So for most of the history of D&D GMs have been free to narrate whatever special effects they wanted for combat, which copious stabbings, cuttings, and brutal bludgeonings. Other systems try to model wounds more directly, but in practice this leads to something called a death spiral where each injury dealt impairs the injured fighter so that he becomes less and less effective, until you are as useless as a screen door on a submarine, but have to keep playing because it's technically not over yet. So in practice HP are the worst mechanism for tracking damage in an RPG, except for all the other systems that have been tried from time to time. <- Apologies to Winston Churchill
So, the exact meaning of HP has never actually been exact, but in spite of this there are always corner cases where it must be acknowledged that actual, possibly horrific damage has been incurred but that the character is still functional. (E.G. Lava. Long falls onto sharp rocks. Weapons with venom.)
Now this was always kind of okay, because up until 4e healing was almost always magical in nature. So yes, Rognar may have just been chewed up and spat out by a dragon, but the Gods fixed him so we don't have to really think about it.
However in 4e, when a character has dropped due to damage, and is in fact dying (making death saves in 4e terms), the narration becomes tricky. If the character is brought back to his feet by a clerics healing spell, or a magic potion, then he could have been stabbed through the lung and brought back and it breaks no ones suspension of disbelief, however if he gets revived by a Warlord with non-magical healing then he must not have been that badly wounded after all, because improved morale does very little to help with sucking chest wounds.
This led to two possible narrative styles: One is often called Schrodinger's hit points, where the actual nature of the injury is resolved not at the time the injury is dealt but only when the character actually dies or receives healing at which point the DM narrates the action flash back style. Or the GM narrates whatever combat description he feels like, and then retcons it if it turns out not to match later outcomes, many people loathe retconning in all forms. Either way it breaks up the flow of combat descriptions that was an ingrained habit of many GMs leading into 4e.
There are other RPG systems where the details of a combat are not known until after it ends, at which point you can assign narrative to mechanical events that occurred within the conflict. At the extreme end you have the Heroquest system where you may not even know if the conflict was resolved with steel or words until after the fact, and less radically in Savage Worlds minor characters survival is determined after the fact like an archer scrounging arrows. But D&D prior to 4e never employed that sort of mechanical-narrative disconnect.
Now 4e not only took a firm stand against "meat points" (Although, ironically, with the bloodied mechanic it became the first version of D&D that actually specified levels of injury in any way), and in addition opened up a narrative-mechanical divide that was new to D&D, but the promotional materials leading into 4e were... needlessly antagonistic to prior editions, and prior ways of playing D&D. So older players were presented not only with a radical change in the way the game was played, but many felt like they were being deliberately insulted for having enjoyed the game the way they had been playing it. It was not a brilliant marketing success.
I'm hoping I managed to sum this up without offending either side (especially considering that presenting it as a merely two-sided debate is a considerable over simplification.)