Mike writes:

Perhaps.. Perhaps not.
The OP asked how quickly the aircraft could reach medical help on the
ground. I believe my experience addressed that question. It is up to
the PIC to determine the extent of the emergency. I suspect that if the
PIC of a commercial flight believed that the life of a single passenger
was in danger unless medical help was obtained soon, the resulting
"flight profile" would be very similar to what I experienced. All the
PIC has to do is declare an emergency.

Declaring an emergency won't get you down much faster, and things like
anaphylactic shock or cardiac arrest require immediate treatment, not
treatment after a half-hour ride to the airport and taxi to the gate.
Additionally, endangering other passengers for the sake of a single passenger
is a bit Hollywood as well.