F33D said:
Sure. Doctors kill patients by the bus load load in real life.
Doctors, yes. Surgeons cutting somebody open or administering complex drug interactions.
EMT-Bs may fail to save a patient, but they rarely kill them.
In real life it is highly unlikely a patient will be killed outright by incorrectly administered first aid IF the patient wasn't going to die without assistance anyway.
A failed Heimlich Maneuver doesn't kill the patient, the choking does. Failed CPR doesn't kill the patient, the heart attack does. Improperly applying a tourniquet doesn't kill the patient (unless you apply it to the neck for for a head wound), the arterial bleeding does. Improperly applying a airtight dressing doesn't kill the patient, the wound and resulting tension pneumothorax does.
The only ay I could see basic first aid actually killing a patient is if it impacted an already serious condition, such as a cervical or thoracic spine injury or severely broken ribs... where moving the patient improperly might worsen the injury to the point of death. That sort of injury is so severe that, in game terms, the patient is headed for death without successful medial assistance anyway. Having the failed roll CAUSE additional injury is probably pointless. The failure merely fails to save the patient.
ETA: I suppose that a completely untrained person using a default might do something that would cause additional injury leading to death, like applying the neck tourniquet, but extremely unlikely for anyone with training.
I'd have a failed roll by a trained individual not provide any healing, and make future rolls more difficult. For a non-trained individual, I'd have the same and an Exceptional Failure cause an additional point of damage as well.