Cooperative storytelling is not necessarily saying yes to anything anyone else says. It's trying to build a story together. To those who say that D&D isn't about that, well we do it frequently at our tables for D&D, and it works fine, so I don't think that it's D&D per se that prevents it. If you feel it's not for you and you prefer another style, then by all means play according to your preference of course.
In the example of the dying man:
We have to assume that hit points may represent something else than actual wounds.
This dying man's hit point loss represents actual wounds, mind you. Otherwise he wouldn't be dying. But hit points, generally, can be anything among or a mixture of wounds, stamina, endurance, morale, psychological strength, etc...
With this basic assumption, when the level 3 PC cleric heals his fellow PCs, he's not necessarily putting back together a dismembered ally. He may be acting to give back some strenght, infuse with energy, AND/OR close actual wounds. But if someone were to have a lung perforated by a long sword stroke, perhaps our level 3 cleric would be unable to heal him altogether.
"But what if a fellow PC has his lung pierced?" you ask. "The cleric should be able to heal him, since any non-dead fellow PC can be healed. Anyone who is not at -10 or minus his bloodied value, can be healed. Period".
Okay, first of all, relax with the math

The game is not about math, it's about having fun playing a RPG. Math doesn't rule the game, you do.
With this said, how could you, as a player, explain what's going on? Perhaps none of the wounds suffered up to now by PCs were pierced lungs? Work with the DM a bit here, that's what cooperative storytelling is all about. Find an explanation.
There are essentially two ways to react to any given statement by a DM:
(1) this makes no sense because... (insert explanation here)
(2) this makes sense because... (insert explanation here)
Cooperative storytelling is about trying to fit #2 intot he game as much as you can.
It doesn't mean you HAVE to accept EVERYTHING everyone tells you. It's even fun to throw an oddball at the players (or the players, at the DM) to see how the other person will react, through the character he's playing. But generally, the idea is to try to avoid pushing someone into a corner he can't get out of. If you do the latter, you reach an RP dead end, and that's what you want to avoid.
The example of the dying man here is arguably cliche, I'm not fond of this kind of story element myself. I guess my point is: if the DM really, really wants the man to die AND the man to be uncurable AND the man to still provide informaiton with his last breath, it should be easy enough for the cleric player to get it at some point and roll with it.
Now I hear those who say "well, why doesn't the DM pick up on the cleric player's proposed story element to cure the man and allow it?" My answer is: I pretty much agree. I don't like predetermined story elements such as "this NPC will die and provide info with his dying breath", I'm more inclined to steer away from that kind of thing and see how the action pans out before deciding on anything.
BUT: assuming you, as DM, want to impose that story element because you feel that the game will benefit from it, then the player needs to know when to accept that what he does won't work, and play along with the new information provided by the DM. No need to pout or be frustrated, there are many instances where the player's actions don't work out, e.g. trying to jump a gap, identify magic runes, convince a NPC, find an item hidden in a room, and the player doesn't succeed. The player needs to accept that healing, like any of the above, can be a failure sometimes.
So in cooperative storytelling, as with any other human interaction, there is some measure of intuition to be used, of trying to sense what the other player (or in-game character) is trying to do, and picking up on that. There is no die roll for that, and success will not always be achieved either; it's just a direction you can take as a player (DM included), taking into account that the DM directs many plot elements and will have final say on what works and what doesn't. If you're looking for a 1v1 match with both players on equal footing, chess or other board games are better suited for you
