There isn't a definition of "passenger" in the carriers liability legislation, but there is in the civil aviation regulations.
The fact that there is uncertainty about these questions within and between the different pieces of legislation, notwithstanding decades of "simplification" and thousands of pages of new regulations and other rules, is the problem.
It's still "guess work".
I'll demonstrate: What if all the patients are mentally unstable and the nurse's job is to keep them under control so they don't try to take control of the aircraft or open the emergency exits? Sounds to me like a function that's essential to the safety of the aircraft, whether the nurse has been "assigned for duty" by the operator or someone else.
I don't know the answer. But that's the point.