Albeit a different airline, our Departure Alternate minima are exactly the same as those stated by Capt PPRuNE. That is 250 NM with all the same provisions.
Perhaps your chances of surviving depend on the company you fly with ?
Agree with most of the comments. The passenger would be attended to by the cabin crew. PA's would be done for medical assistance etc. The aircraft would be diverted to an airport at which it was both safe and legal to complete a landing.
Hard to imagine a suitable airport being 2 hours away except in the Etops situation but in such an event, then that is de-facto and the pax would have to be attended to for the time it took to get there. If the situation arises where it is necessary to ignore limits and thereby compromise the safety of the flight, it must be for a position of serious jeopardy. As harsh as it may sound one pax with an illness however serious doesn't really fall within that definition.
IMHO !