It's pretty rare for a party to have no at least theoretically magical resources. Any non-Martial leader can claim that they perform some sort of off-screen healing magic which can't be done during a short rest. ("I have woven the charm of wound knitting, but you must do nothing for the next few hours so that it may work.") As for martial leaders... "A rangers hands are healing hands", or at least, a Warlord's are.

You can claim he's used useful herbs, bound your wounds so that while you're still "injured", they don't actual affect you, and so on.
I personally find it more difficult that there's such a thing as "real" injury - you've got crippled and blinded NPCs all around - but nothing like this can ever happen to the PCs. Then again, no version of D&D ever had any "official" rules for crippling or long term injury.
The other factor is that hit points, as always, represent more than just physical injury, and healing surges represent a mix of luck, resolve, inner strength, adrenaline, and "spirit". (Thus undead drain healing surges, literally taking your will to live.) So someone at low hit points and out of surges might have no wounds other than shallow cuts, bruises, and so on, but he is at the end of his rope -- he can't fight on anymore, and his ability to dodge blows, parry weapons, and duck is very reduced (low hit points, so any attack is a serious one).
As brain-blasting as the 4e healing mechanic is, the fact is, it just formalizes the way 3.x games were, usually, played -- someone just breaks out the healsticks when the fights over. If you like, you can imagine this is how it is done in 4e, you just don't pretend to be tracking the charges.