I'm running the game very much Rules-As-Written: if the book says something can be done the players are free to do it. Works the other way too, I roll in the open and don't pull punches. That's kind of why we noticed how the recovery rule could be abused, but this is one case where we haven't done everything the rules theoretically allow
Anyway, thinking here if it can be made to work in the game fiction and with the rules... Rolando, I like your idea of "damaging healing". Thinking about that, let's say that the character with 4 damage (1 left before incapacitated) would have hurt their knee. The first aid could be something like violently pulling and re-setting the knee. This would hurt like hell, would cause 1 damage and if it fails the character can't walk (=incap). On Medical Aid roll the best result would "cure 3 points" but yes, that is a lucky roll it can't be rerolled unless the situation or equipment changes. Hmm, I think here I would also be strict with modifiers, eg. bad conditions for perfoming the first aid would be -1. ... Yeah, that's the only way I see this could be justified in theory. I think we'll continue to smile at the loophole and not use it.
By the way, game story time! The doc in the group is a good one (AA) and has been usually succeeding in the Medical Aid rolls. Except on the last session. His best buddy got a 10 crit in legs and the doc got quickly there to stabilize ... but failed. Pushed, but failed again. So it was time for a death save - with a single d6. STR D and
no Stamina. The buddy failed, pushed ... and still failed. The doc's best friend basically bled to death in his hands, in a dark rainy forest after midnight. They had been ambushed while trying to scavenge parts from destroyed vehicles (they even had a lookout - who failed the Recon roll completely). Lot of failed rolls in that session! This was our 15th session and the first player character death - it actually hit them hard "we can really die any time".