I don’t think it is as black and white as you describe, in terms of medic vs. nurse. It depends on the situation in front of you.
Personally, if I was in the situation of being seriously ill on a plane, I would want to know that someone could effectively triage the immediacy of the situation (appropriately trained medic or nurse). In the UK, in A&E (Emergency Room settings) the Manchester Triage System (MTS) is used widely where as the Emergency Severity Index (ESI) is widely used in the USA. They broadly deliver the same intent, which is to address 3 key questions in the context of multiple patients, but the rationale also applies to the individual.
1). Who should be seen first?
2). How long could / should a patient wait before need of an intervention?
3). What resources are required to stabilise?
Once triaged, there are a variety of Life Support training courses and qualifications addressing Basic Life Support (BLS), Advanced Life Support (ALS), adult or paediatric versions including support for the pregnant woman if this is the situation. For situations related to traumatic injuries, the Advance Trauma Life Supoprt (ATLS) qualification also exists.
I don’t mind whether it is a nurse or physician that looks after me, provided they are trained to triage and trained to stabilise. I would not impose on a psychiatrist to assess a traumatic injury, but an ER trained nurse with ATLS would be highly appropriate. The reverse exists in that I would take the assistance of an anaesthetist over an ER nurse for an airway issue requiring intubation.
To go back to the original point… I don’t know of any of my medic or healthcare colleagues who “seek” recompense, but they do want to know that if they offer their services, that this is accepted as being provided with the intent of helping, and provided they do not do anything negligent, to not be sued for any undesirable outcome that may have occurred anyway without their intervention or more importantly for an adverse outcome that is an unintended part of the treatment.
An example of the later would be to administer cardiac life support but breaking a rib on the patient, which is not an uncommon event in providng chest compressions to elderly women with low bone density.