This is nowhere near as simple as some would like to present it.
Firstly, the passenger himself is not going to be making the call to divert or not. End of story there.
An A380, just after take off from Singapore (to London) would be roughly five hours away from being able to land. Fuel dump would take about an hour, but that still leaves you 50 tonnes above maximum landing weight. So, if you start dumping immediately, you could land in the middle of India (do you really want to be there) or perhaps Dubai. If the dump starts later, you actually end up having to go further before you can land....basically at the end of the dump you're always about 4-5 hours away from landing (at least if you want to be below MLW).
Yes, you can declare an emergency, and land above max weight, but the question is, of course, what emergency...there's nothing wrong with the aircraft, and doing so exposes all of the passengers, and the aircraft, to an unquantified extra level of risk.
Once it starts down the track, there are a surprisingly small number of airports available to it. Between Singapore and Europe, only Hyderbad and Dubai are readily useable. Others exist of course, but they're for the days when the aircraft needs to land immediately, not an individual passenger. In this respect, the A380 is much more limited than the 747.
The call to divert or not really rests with the captain. Of course, some airlines will pretty much take that out of his hands (although I don't know SQ's policies here). Medical on the aircraft is helpful, but is unlikely to be used to make the final call. Emergency medical advice, geared towards the needs of aviation, is available from a company in the USA (and there may be others), as long as your own company uses them. They make the call medically, but it still rests with the captain to make the final call. Would you go against them...well yes, you might. They will base their call on the medical situation, and upon the known medical facilities on the ground, but the overriding concern is always the safety of the aircraft, and all of the passengers. For instance, with a heart attack patient, if Manila were 100 miles away, and HK 500 miles, but Manila was in the throes of a typhoon, which call would you make?
In a 747 you could dump just about all of the fuel, but in an A380 you're always left with about 85 tonnes remaining (about 440 tonnes all up). This whole scenario is not simple. For instance, say we land overweight, but it goes a bit awry, and we end up off the far end of the runway...what about the duty of care to all of the other passengers?
What would I do? Well that answer is dynamic, and depends upon the advice I get from Medlink, the weather and other conditions relevant to my airport options, and of course, just how heavy the aircraft is.
