Just to clear some things up, there's no reason to believe this person is lying about their circumstances unless you have reason to believe so, especially seen as you met them in their role as an emergency medicine doctor and they have treated you themselves.
Let's say this man went to medical school at 18, and completed a 5 or 6 year MBBS (or equivalent) degree. He would have graduated medical school at the age of 23/24. Doctors must then complete 2 years of foundation training. The pathway after foundation training to become a consultant (gain your CCT) in emergency medicine is 6 years minimum, although many emergency medics train less than full time and many doctors have breaks in their training.
For arguments sake though, after foundation 1 and 2, he would be 26. At 32, it is perfectly reasonable that he is still on the training pathway. With regards to exams, doctors take exams throughout their careers, mostly Royal College exams. To gain your CCT in your speciality and become a "fully qualified" doctor, you have to pass a number of notoriously difficult exams which many doctors take more than one attempt to pass.
In terms of whether or not he is interested, time will tell. Just some peace of mind for you here that you haven't been led down the garden path and what he's told you about his profession is really not difficult to believe. I wouldn't wait around for 6 months though.