Lets say a skilled medic (say 30 or 35 int) who is trained in medicae wants to treat a patient in the field who took a bullet (we'll be generous and say only 2 points of critical damage). It looks like they would be suffering about a -10 penalty to their check (probably have assistance so no penalty, +10 base check for extended care, -20 for critical wounds). This check is most likely to fail which forces the patient to make a toughness check or take a point of damage. If they're critically wounded then they take critical damage and die.
So if a guy is recovering in the field from a minor bullet wound, the attention of a trained medical professional is far more likely to kill him than it is to help? It also seems that the worse your wounds are, the more desperately you should avoid doctors.