Standard procedure in some parts of the world (a luxury in others I know) is for the crew to have the option of having a doctor speak with the boat and to then advise the pilot in command on whether the casualty is in need of urgent assistance. In my experience waiting a few hours in generally acceptable.
Whilst needing medical confirmation of need is surely mandatory, IMHO the doctor 'advising' the pilot is a recipe for unacceptable risk. Doctors are not qualified to assess the risk of a mission. They are only qualified to decide or estimate on the medical condition of the patient. So a doctor can decide whether the cost is justified, whether the organisation's protocols are met medically, and whether the medical risk of a transfer is justified - every transfer has a defined risk of death and morbidity even in CAVOK conditions twin pilot IFR equipped.
Only the pilot can decide whether the mission is within acceptable limits. Those limits may be different for a military mission than a civilian one, but that is an aviation decision not a medical one
The only safe operational tasking is to have a Chinese wall between the medical and aviation decision whereby each decides on go/no go independently. You then launch only if you have two goes. If you allow doctor and pilot to discuss you inevitably put pressure on both. We did this in Dallas in the 1980s, launching into what I now know to be unacceptable conditions because the patient was a child, because the patient would likely die without us. Often the pilot said no, then asked about the casualty and said yes......Back in the UK we operated a Chinese wall. We lost missions and I dare say patients suffered, but we didnt put a crew of three let alone people on the ground at risk for one patient.
To those who have heard me rant on about this ad nauseam, my apologies, but the lesson still hasnt been learned