To be entirely fair, what you describe as position #2 is often a strawman as well. What you describe as position #2 is the far end of the HPs can be not meat spectrum. It is an example that is often used by people who use HPs as not meat to illustrate how far they can go under the constraints of the system if they choose to. Consequently, some people have taken the notion that all people who use HPs as not meat go that far with it.
In all the games that I have DM'd and played in, it has been rare that all HPs except for the last blow are non-meat. It has happened, mind you, it's just not something that happens all the time. Usually, what I end up with (not just in my own narration as a DM but in my experiences as a player) is that some instances of HP loss will be described as veggie-damage (i.e. no meat) and other instances of HP loss will be described as both meat and veg in varying proportions.
It's also worth pointing out that the part that I bolded isn't entirely accurate because the severity of the injury doesn't need to be minor. I use a wound system based on 4e's disease tracks, and a character who falls and breaks her leg can recover all of those HPs and still have a broken leg. The modified disease track models the impairment of the broken bone instead of the HP loss modeling it because HP loss was never intended to model specific injury like that.
I also have an example from old-school D&D: losing a limb. Losing a hand or an arm is a pretty severe injury. And yet, your maximum HP total doesn't diminish when you lose the limb. You can recover all those HPs and still be missing that limb.
Now, I write this not to try to convince you to view HPs this way. How you do things is naturally your own business. I just wanted to provide a little clarity and a little additional perspective.