Thought I might just add a "data point".
I've responded to a number of requests (on QF and VA FWIW). At one stage I had a strike rate of about 1 in 6 flights for the "is there a doctor on board" page.
A couple stand out:
I spent most of one MEL-BNE with a woman with severe vertigo and subsequent nausea and vomiting, who was very sketchy on details of her medical history - I suspect she didn't want her connecting international flight to be cancelled. I was asked (via the cabin crew) if it would make a difference (to her condition) whether we diverted to SYD although it was only going to be a few minutes shorter than continuing to BNE so I suggested to proceed to destination. The captain was reportedly happy with that (I realise at the end of the day that isn't my call to make and he'd likely consulted with ground advice in addition). She happened to be sitting next to an off-duty FA and a spare seat so that made the whole situation more manageable. The flight was otherwise full. There certainly was plenty of "kit" available to use although I elected not to give her any drugs as the pax was a bit sketchy on details including allergies! Very grateful cabin crew and an ambulance crew waiting on arrival. I was clearly the only (by title identification on the manifest) doctor on the aircraft (the crew were lingering near my seat debating whether to announce or just ask me - I overheard the crew so just asked them if I could assist them in some way!). No-one else noted the situation and enquired / volunteered to assist so I assume I was genuinely the only medico on board.
Another MEL-BNE, I identified myself after a call for a doctor and proceeded to the front of the cabin - I followed up the aisle a (very young looking) doctor to the front (I considered she may be very junior and be grateful of assistance). When I enquired as to her qualifications (to assist a pax who was short of breath), she was starting as an intern in three weeks time! As I was a medical registrar at the time I felt that (presumably) "trumped" her ability and had started to speak to the unwell pax who was sitting on the crew seat, but fortunately following me up the aisle was a respiratory physician so I gratefully left it to him to handle shortness of breath! The pax subsequently returned to his seat and the remainder of the flight was uneventful.
Another one domestic flight was a man with severe liver disease having a hypoglycaemic attack. His travelling companion was clueless as to how to manage it and he was getting confused and drowsy. Easily solved although it was borderline getting some lemonade into him as he was getting very drowsy!
Internationally have been on flights with a couple of calls for assistance, identified myself and there were multiple doctors on board so they took my details (including area of specialty) and then would come back later to advise me that someone (based on sketchy details given to me - someone appropriately qualified) had dealt with it. In one case they ran through the scenario as my specialty has some overlap with the clinical situation but it had been handled by another sub-specialist appropriately.
<touch wood> never been on a flight requiring a medical diversion </touch wood>
Not once did I worry about indemnity at the time, but they have all been on Aus carriers. I'd still volunteer on a non-Aus carrier, but would be very cautious about any intervention (eg. drug administration etc).
My experience has largely been that most pax who become unwell have pre-existing conditions that cause the bulk of symptoms that they experience in flight, but they have little clue how to manage their situation themselves (where appropriate) (eg. the man having a hypo and he/his companion not recognising it - turns out they had traveled for ~14 hours without eating!). That may say a bit about the discussion/education given to them by treating practitioners than the patients themselves, including discussion of plans to travel with complex medical conditions, although there is certainly an "I'll be fine" factor and personal lack of preparation for basic contingency plan "in the event of". The true "totally unexpected" would seem to be a rarer commodity (and fortunately I've not had to assist in that sort of situation), although I am aware of colleagues who have attended pax with (unexpected) heart attacks and strokes in flight.
I have confirmation from my MDO where the good samaritan act (or equivalent) does not cover me sufficiently, they will provide cover provided I have practiced in a way that would be assessed as "reasonable" within Australia and in line with the good samaritan act (whether it applies in the country of travel or not).