Indeed it is not a PADI medical form, it's a consensus agreement between agencies who subscribe to the RSTC (Recreational Scuba Training Council)
A medical with a "Yes", properly signed and/or stamped by a physician should be all that is required for the counter staff to accept the person for training, HOWEVER, it is still down to the instructor's discretion. I will quote from the PADI instructor manual (2009 electronic version, General Standards and Procedures, page 6; bold type is the "standard"):
a. Any question of medical fitness is solely the physician’s area of
expertise. Ultimately, however, you have the right to make the final
decision about who you will accept into your scuba course after medical
approval is obtained. Instructors have no obligation to accept
every applicant.
This means I cannot medically diagnose a condition but I can still refuse a student even if signed off by a doctor, if I think the student might be at risk underwater, or I might require the student to get a second medical from a local hyperbaric physician whose judgement I will take over a general practitioner with no diving experience.
For example: A recent student of mine had obtained clearance from his GP in the UK prior to arriving at my dive centre in Egpyt. His GP had signed his medical with the following "student has asthma, but good lung volume" and was cleared to dive. I am very sorry to say that this doctor clearly has no idea what he was talking about when it comes to diving and when I questioned the student it was apparent that a proper test had not been conducted. I could have refused him, but I sent him to the local hyperbaric physician who did indeed clear him to dive after conducting the appropriate tests. I *still* could have refused the student, but I didn't. (BTW please let's not get into a discussion about asthma or other conditions here)
It is not an agency issue, be it PADI or anybody else. Some divers, when presented with the medical, refuse to go ahead with the training. Some instructors will get the student to cross out the Yes and write No. I will not compromise my job security and risk a person's life for the sake of a few extra bucks, and I have indeed had to turn away students, and lost personal income as a result.
If it's a matter of confidentiality (I had one lady with a bipolar disorder who was uncomfortable declaring this on the medical, and other students with serious medical problems that prevented them from diving) then I will treat it with as much confidence as possible, but aside from me, several people at the dive centre need to be aware of underlying medical condition just in case something really does go wrong.
Hope that helps clarify things a little,
C.