Rex,
Although you can put an aero med fit on most civil types the set up on the Tri Stars and C-17s allows for a complete CCAST (Critical Care) setup allowing the patient to be accessed as if in a hospital and although the C-17s take the majority of critical patients the Timmy still handles its fair share, as well as those less seriously injured who still require a stretcher. Unless dedicated to the role most civil carriers place the stretchers onto lowered seats which are not ideal for the patient or the aero med team.
Back to the original topic pax have to seek permission via PJHQ to leave the air bridge, and this is not often given. If pax do decide that a civil carrier suits them best then (if permitted) it is explained to them at great length that this is not a recognised route and they will have to pay for their own transport. The poor mover caught between PJHQ and the angry passenger is only the messenger, not responsible for the delay/ash cloud Greek ATC/broken aircraft, yet it is they who receive the brunt of the flack.
On another note the 216 crews will always offer to explain to passengers why the plane is broken or some country or other won't let us over fly them this week.