A model that takes its last wound is not, necessarily, dead. It is incapacitated and is, for all intents and purposes, out of the fight.
Medics do not "heal" a model. Rather, they assess the extent of the wound(s) of the model. The Medic SA represents this like so; if the Medic makes his roll, the wound is not grave enough to remove the model from the fight, and he tells the model, "Ain't so bad - now git your arse back in the fight, soldier!" If he fails his roll, no amount of first aid will return this particular model to combat status - "Hang in 'til I can get you to the aid station, Private!" "Hang in soldier, you're gonna make it (no, he's not)" "Oops...heh, no worries. MEDIC!"
Being a former combat medic in the US Air Force, I can attest that this is what I did as a medic. I assessed, and, if able to get the soldier back in the fight, or stabilize him/her until he/she was able to receive better care, treated the immediate injury. In the case of GSW's (gunshot wounds), if it was non-life-threatening, I would get the bleeding under control and apply a compressing bandage to keep blood loss at a minimum. If there was a great chance that the soldier was going to die, I would not waste valuable medical supplies if they could be used to save another. This is what triage is all about - doing the most good for the most patients. The mnemonic we used was DIME - Delayed (treatment could wait, non-life-threatening), Immediate (treat now in order to save life/limb - may be downgraded to Delayed or Minimal if first-aid stabilizes patient), Minimal (put a bandage on it and go), and Expextant (expected to die, no matter what course is taken).
Examples:
Delayed - broken leg, loss of an eye, laceration with some loss of blood, loss of hearing, 2nd degree burns, etc.
Immediate - 3rd degree burns to less than 75% of body (cover and keep cool with water), blocked airway (perform tracheotomy and restore airflow), severed limb (tourniquet), sucking chest wound (tape a credit card or something similar across hole in chest leaving one of the four sides untaped to keep blood in, but allow air to escape and keep lung from collapsing), etc.
Minimal - broken finger, contusions, abrasions, 1st degree buns, etc.
Expectant - GSW to head, heart, spleen, severing of carotid artery (can't use a tourniquet here - blood loss will kill brain), 3rd degree burns to over 75% of body, etc. This was a harsh decision, sometimes. "Can the patient be saved?" "Is it worth the supplies to attempt to save?" "Have I made the right decision for the greater good?" "I've gone off on a self-indulgent tangent - let me get back to the question."
This game simulates that by giving the medic a chance to do the above. When the medic makes the roll, assume the wound was considered MINIMAL. No other medic is able to do any greater good, as the wound has been assessed and dealt with. If the roll is failed, assume the wound was assessed to be one of the other three categories. Again, no other medic would be abe to help, as they would tend to agree with the assessment. Having the medic in the squad allows the assessment to be made. Without a medic, the soldier is left to their own devices. Wounds cannot be assessed and are assumed grave enough to removed the soldier from the fight.
The Ticker is a one-use item that can only be used to return a model's last wound. Once used, it cannot restore another wound, even if the model regenerates wounds or is "healed" afterwards. Regeneration is a special ability of the model, itself, and is separate from the medic ability. Powers are just that - Special Abilities that confer unnatural abilities. In game terms, they are above and beyond the powers of ordinal mortals.