I suspect a US court would take jurisdiction of a dispute between an American doctor and an American patient.
It’s happened. As you might imagine, there have been a lot of lawsuits between Americans concerning things that have happened in foreign countries. The courts clearly have jurisdiction over the people since they a are both Americans. The only question is whether you apply US law or Mexican law. I think the argument could be made (and has been made successfully in the past) that the court should apply US law when the dispute is between two Americans. Usually the argument is that the foreign law is stupid or difficult to determine and it would benefit both parties to use American law that they are more familiar with. In this case that argument might not make sense because the doctor is likely to say that he did it in Mexico precisely because he wanted Mexico law to apply. That’s a pretty good argument but not necessarily a slam dunk.