I've responded twice on TATL flights. As an inpatient/outpatient PCP, I don't hesitate at least to assess the patient (and would always defer to a specialist with relevant expertise).

On a UA flight to Europe, we had just tucked into dinner when they called for a doctor. A teenager with a tree nut allergy realized that the butter chicken she had just eaten contained cashews and the FA wanted to know whether we needed to divert before we headed out over the Atlantic. The girl looked a little nervous but otherwise fine. She had an Epi-pen (though only one) in her carry-on, so I said I thought we were fine to continue. All ended well. The FA who had served her dinner was very grateful--she confided that she had misunderstood the patient's query about the contents of the meal and had in fact never heard of a "tree nut." As I recall, her iPad app offered me $150 or some miles. I always introduce myself with my specialty, and the girl's mother must have googled me, because a few weeks later a tin of popcorn arrived at my office with a thoughtful thank-you note.

A few years later on an AA flight home from Europe, they called about a nice older man with COPD who was short of breath. He should have been traveling with oxygen, and the FA had already hooked him up to one of the on-board tanks but was worried about running out before we landed. The purser and I did a back-of-napkin calculation that we would have enough O2 to make it with one tank to spare in case anyone else needed it. I checked on the poor guy several times over the remainder of the flight; he did fine. I also helped the purser fill out a long form with lots of questions about the patient and a few about me. Shortly before landing, she presented a bottle of champagne to my wife, who had to entertain our kids by herself for much of the flight. I got an email from AA's Chief Medical Officer two weeks later and 25k miles arrived in my account.

In neither of these cases did I add much more than reassurance to the crew that we were OK to proceed. I'm happy to help if I can and would never ask for anything in return and am not concerned that an unsolicited travel/mile credit would invalidate any Good Samaritan protections. Having said that, I appreciate all of the medical and legal perspectives on this thread!