Not so. I had a student with diabetes come to me a couple years ago. Well controlled with a pump and never had an issue with sugar getting out of control, their doctor said they were a good candidate for scuba. I called and asked NAUI if I could train them. I was told "You have to make the decision BUT if ANYTHING EVER happens to the student underwater in the future we will pull your insurance and leave you liable for any claims made by the family." As much as I enjoyed the person's personality and would have enjoyed training them they weren't worth leaving myself exposed to a civil or wrongful death lawsuit where I could lose everything my husband and I own.
I know the YMCA had (has?) a nice program for diabetics that's basically a research program they sign up for. Diabetics get to dive AND provide information so we may better understand how the disease affects divers.
So the translation is: have the instructor check with their insurance company / cert. agency on it.
My understanding is that with the PADI insurance as long as you have a physician's release and the diver was as honest with the doctor as they were with you (i.e. completed the RSTC medical questionnaire, took that to the doctor to have them sign the physician's release section), the instructor will not be held liable. You can still refuse to train the diver, but it boils down to a "not on my watch" situation.
Truthfully -- if the primary care physician has signed off on it, and there is an understanding that the diver knows how to manage the diabetes, there should be no problem. I, as an instructor, might follow it up with the physician if I had concerns and say something like this: "I see you signed this release for diving. I just want to make sure we're on the same page. The reason he had to see you was because of his diabetes. The reason diabetes is contra-indicated for diving has to do with the change in metabolic rates at depth as well as the potentially fatal repercussions of a momentary blackout or convulsion. This can be a high-stress (physical and mental) activity. I'm not pretending to know more than this or to do your job, just that I wanted to ensure you were aware of the extended stresses that may be present and offer you an opportunity to withdraw your medical clearance."
A lot of doctors don't realise why they're signing something, and in many cases, the instructor knows more about why a medical condition is contra-indicated than a doctor. That doesn't mean that we know when a case doesn't warrant the contra-indication, it means that we know why most, many or some cases are contra-indicated.
As for the exact situation -- the primary thing I've heard mentioned with diabetes and diving is to avoid a pre-emptive compensation for the time spent underwater. Many diabetics have apparently run into trouble by sugar-loading before the dive then ending up in a hyperglycaemic state during the dive.