I don't see this getting resolved in our conversation, because if those rules I posted are correct, then it's very clear to me that you're house ruling in favor of narrative coherence. While I understand the motive, I dislike that it needs to be house ruled to achieve.
That is, if I want to "check" an ally, it doesn't mean I want to start to stabilize him. You say that the "stabilize the dying" action covers the narrative portion of checking a creature, where the mechanics disagree (as far as I can tell). This specific action seems intent on stopping the character from making death saving throws. I was asking about merely
inspecting the wound, and nothing more.
To that end, I still hold that you've house ruled it as one and the same, "you didn't patch them up, you just discovered that they aren't bleeding out." I have two issues with this.
(1) It's a house rule "fix" to what I think shouldn't need to be fixed in the game.
(2) It's restrictive. It forces the player out of "actor stance" and into a place where he needs to narrate the fiction he wishes. To a group that wants to stay immersed, this is jarring enough to pull you out of a deep immersion state. If I checked on another PC to see if he was okay, and I heard, "do you want him to be stabilized?" I'd say, "uh, I was just curious if he was." I was taking an information-gathering action, and nothing more. I wasn't trying to shape the story other than by having my character investigate, and that's been taken away. By having a separate action that allows you to investigate in-game, you leave both avenues open. That is, you can investigate in-game (and stay in-character), or you can attempt to stabilize someone (and flavor it as in-game or from a more story perspective ["after inspecting him, you find out he's going to be fine."]).
To that end, can't you basically attempt to "stunt" or the like with skills with page 42? Shouldn't this cover areas that skills don't explicitly cover (like checking to see the physical state of a downed character)? If so, couldn't that be used to check the character in-game? And, if the above is true, wouldn't that produce the Schrodinger's Wound problem?
In other words, I think it leads back to being a problem to people that prefer to remain immersed in the game. If you don't mind getting pulled out of immersion (that's not to say the story or the game), it's probably fine (or even great). To others, I still hold that it's a problem.
I don't like that there's no wiggle room for NPCs (they're either unconscious or dead, not ever bleeding out), but that's just preference on my part (narrative paths and all that). So, fair enough on the mechanics (I assumed it applied to more since it referred to "characters", but that was my mistake).
As always, play what you like