In 3E, If my character got knocked down to -7 to -9, I wouldn't bat an eyelid if the DMs description was something along the lines of..."the bolt sticking out of your eye REALLY hurts, you see everyone looking at you (with your good eye) in complete horror as you fall to the ground unconscious". I know that pretty much the only thing that's going to save his bacon is some instamatic healbot attention. In fact, such attention is going to be the only way that he's back up and in the frey once more in a handful of minutes.
If the same thing happened in 4E (bolt through the eye is described by the DM, dropping him to -7 to -9 unconscious), then it would feel kind of weird to make my save, surge up after the combat and be back to full operation (as in my guy has a similar chance of surviving another encounter as the uninjured fighter over there). No divine assistance, just a little bit of heroic grit. I'd ask my DM about the whole bolt through the eye thing to which he'd most likely have to say - "nah, it was just a flesh wound".
What I'm getting from this is that you have no objection to non-divine-healing-generated recovery - as it is possible in 3E, as per the example you give from the Paizo boards - but that you don't like the idea that it is ordinary rather than miraculous. (I'm not sure I agree that 3E makes it miraculous - the DC to stabilise someone with a non-magical Heal check is only 15, after all - but that's another matter.)If left to your own devices (that is no one to aid you), you are stabilized but not yet conscious. You then have to start making 10% chance hourly checks to regain consciousness - losing a hit point each time if you fail. On your own, chances are you're not going to make it - and if you do, it was a ***miracle. In a group situation with a cleric, curing wand or potion, you are going to be getting this divine healing. You aren't going to have people go, "hmmm... let's leave him for a bit and see if he gets better". The bolt in the eye character is going to get the healing and no one's sense of verisimilitude has been upset (providing that such miraculous healing is possible in your game).
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***Such a miracle has never yet happened in a game that I have personally played in. I read a thread over on Paizo where an abondoned -6hp character survived such an occurence (the rest of the party were killed). He came back into town several days later having somehow survived. The circumstance was such that a legend was born. Many whispered that the gods themselves must have got involved.
If that is correct then there is a way of handling it in 4e without the retconning/Black Knight-isms. But it does require divorcing ingame causation and probability from the rules.
The way is this: narrate the use of a healing surge in such a situation as a miracle. Of course, the mechanics don't make it especially improbable. But that doesn't mean that it can't be treated as miraculous in the gameworld.
If this sort of narration isn't carefully handled it does run the risk of the gonzo-ism I've discussed above. I think that this lurking threat of gonzo is inherent to 4e. It's not at all oriented towards gritty, I don't think.