I did once... kind of. It was with a psychology PhD student, though. (Not sure if it counts.)

When I was in university, I was struggling with depression, concentration, and severe anger issues. I had no idea what was wrong with me, but in my 4th year, I finally decided to seek help through my university's counseling services to get properly diagnosed. They told me I would get a free diagnosis if I let them use my appointment as a training session for a graduate psych student. Since it was free, I let them do it. There was a trained psychologist in the room with the graduate student anyways, so I wasn't too worried about it.

edit:
Actually, I forgot... I went to the ER once when I had bronchitis and then developed a severe allergic reaction to the medication I was given. Since the hospital I went to was affiliated with Harvard Medical School, I got a medical student who was in training. The funny thing was, I think the medical student was more knowledgeable than the "experienced" ER doctor. The medical student was the one who realized I had an allergic reaction, not the doctor himself.