As InDaBack stated very very few people are so critical they need to be moved immediately and in most of those cases you will do more harm by moving them. (Spinal cases for example are not a life or death emergency, but need to be properly transported with a neck brace, vacuum mat, etc. you throwing them in a Piper Warrior will more than likely do permanent damage).
The Mercy Flight allows you to break a rule when all other avenues have been exhausted. It does not allow you to take off in to the sunset because you think you might be helping.
If you have ANY form of contact with the outside world... Telephone, Satellite phone, HF, even VHF on 121.5, your best option is to call the aeromedical organisation in your state. They are in a much better position to make the judgement call on how best to handle the situation and task the appropriate resources. (No runway lights for example may mean an NVG equipped helicopter is tasked instead assuming the patient can not be appropriately managed until daylight)
Would suggest the Mercy flight rule would actually be most applicable to aeromed operators who have the resources (aviation and medical crew working together) to determine the safest possible outcome for both the crew and the patient and take the "all other avenues" cause far more seriously.