Whoops, I should have had more sense than to rush into a sweeping statement, and I accept most of your responses. There are, of course, two reasons for an aircraft deliberately squawking A7700: decision by the crew, and crew response to advice from ATC. I overlooked the latter when considering the medical emergency scenario.
I'm years out of date, but my feeling is that a crew would generally only squawk A7700 of their own volition if declaring a MAYDAY. My old books state this is when the flight is subject to "a condition of being threatened by serious and/or imminent danger and of requiring immediate assistance." This is defined as a Distress Message, and I don't think it would be appropriate for a medical emergency (unless it affected the conduct of the flight, as it might in the case of a flight-crew incapacitation).
The lower state of emergency, defined as an Urgency Message, is issued in the form of a "PAN" message when the flight is subject, my books state, to "a condition of the safety of an aircraft or of some person on board or within sight, but which does not require immediate assistance." Most medical emergencies fall into the PAN category, in my opinion. In this case, unless procedures have changed, I don't think the crew would select A7700 unless asked to do so by ATC. If they do, so much the better, and the flight can be assured of red-carpet treatment.
We have no details of VS24's problem. Speaking generally, however: if the FQIC (fuel-quantity-indication computer) had suddenly showed, for example, that the estimated fuel remaining constituted less than 30 mins endurance, any crew would squawk A7700 and declare a MAYDAY immediately. If the FMC (flight management computer), using suddenly-changed information from the FQIC, calculated less than 30 mins endurance over the planned destination, this would also constitute an emergency. Whether the crew would declare a MAYDAY or a PAN would depend on the precise circumstances and the judgement of the crew. Having said that, it is much better to declare a MAYDAY and subsequently downgrade the emergency to a PAN than vice-versa.