ETOPS,
Satphone perhaps, but isn't your employer one of the ones to cease ACARS use as a cost-cutting measure after 110901? A great leap forwards.....
Returning to the main thrust of the argument, as the aircraft commander, I must say that in the majority of cases, the presence of a doctor on board who presumes to treat a sick passenger only increases the exposure to risk. Better, perhaps, to divert straight away that the cabin crew say the passenger needs serious attention, rather than involving individuals who may or may not be who and what they say they are and may or may not expose the commander, crew, and airline, to risk of claims.
The decision to divert in these circumstances is a very difficult one, not least on account of the paucity of accurate information available.