what would have happened if the passenger's condition was such that a medic would advice an immediate diversion. It would be very difficult to explain after your passenger dies as to why you didn't take medical advuce when it was standing right in front of you.
Well in the contect of diverting for medical reasons may I make a general point that the volunteer medic on-board will almost certainly not have the big picture, and the crew and most especially the captain has to weigh up the risks of continuing the flight for the ill pax against the possible risks of diverting ASAP because that is what the on-board medic is advising..for example:
The nearest "obvious" airport on the map may not be the best option from a medical POV. Often flying another 15-30 minutes or more to airport B rather than landing ASAP at airport A might mean the patient gets better medical attention quicker.. this is where the ground based medical advisors on the sat phone come into their own because they know where the best facilities are.
The nearest obvious airport(s) on the map may be a very poor or even illegal option from a weather/equipment point of view and a diversion may place
everybody on board at serious risk ( northern canada/Russia in winter are classic examples).
It can be a difficult decision to make and is the sort of scenario often discussed during command upgrades, especially on Long Haul fleets...