This has certainly been a well responded thread.
When I took NAUI OW I in Singapore, the LDS referred all students to a doctor who specialized in diving medicine. The examination included a chest X-ray, the usual medical history interview and an ear, nose and throat evaluation. I was only 42 and in pretty good shape so I don't know if the examination got more involved for older people or people with contraindications.
In theory, there were no exceptions; get signed off by this particular doctor or no diving.
Except... One fellow managed to skip past the exam. He also failed to mention he had had some kind of upper respiratory problem the week before class started. So, upon surfacing from the first open water dive, he was coughing blood. Not a good sign!
I still remember the sight, 21 years later. We were diving at Pulau Hantu (Ghost Island) - a little irony there... I surfaced aft of the stern of the boat and the instructor was on the port quarter and the diver was on the starboard quarter. They couldn't see each other but I could see the blood. I told the instructor about it and he was dumbfounded for a moment. Like he didn't grasp what I was saying. He got the strangest look on his face as he swam around the boat to survey the problem.
AFAIK, everything worked out fine but the student never returned. I suspect that the instructor had a bit of serious introspection re: how he managed to let a student slip by the medical. I doubt that it ever happened again. Still, what if the student had the exam two weeks before the OW dives and developed the condition after the exam. The results would have been the same.
What to do about the form? Privacy isn't my biggest concern with the form. The fact is, I am not an ideal candidate for dive instruction (that's a nice way to phrase it). However, my Dr did said that he would have no problem signing off on my medical conditions for diving. I wonder if he really knows what is involved? I wonder if he has ever done any diving? He certainly knows what meds I am taking and why.
In the end, I make all of my own choices. It's worked out pretty well so far.
Richard