Insulin dependent diabetics can't effectively produce/regulate insulin production to increase/decrease their glucose levels. This can lead to convulsions underwater. While problematic on the hard, these can be deadly in or under water.
I'm not playing "doctor" here, but I am acting as a dive professional. Should a doctor clear an insulin dependent diabetic to dive, I want to know WHY. I also want to know that they are insulin independent. Should the doctor be wrong and the student start the shakes underwater, I need to know what to look for as well as what to do. Getting them to the surface is a no-brainer, but what then? Why would I allow ignorance to put me or my student into that situation? Moreover, if I'm not aware of a particular condition, I won't know what to look for. People go into denial all the time when things go wrong underwater. If you don't know, then you won't be looking for those sometimes subtle clues.
Just because a doctor says a condition is diveable doesn't mean I HAVE to teach them, especially if they are unwilling to let me know what it is. I teach adaptive Scuba so I have to deal with doctors and divers who have no clue all the time. There are many conditions I can dive with... most days... with benign conditions. But not knowing about that condition puts me at a disadvantage and my student's health at risk. Maybe a certain condition requires an extra buddy. Maybe it requires a few extra buddies. If a diver is unwilling to let me know what the condition is, then I am unwilling to teach them. I can teach/dive with a legally blind diver with an extra set of eyes and fins. Autisitic? I need two and so on. I can't make those decisions that impact safety if I'm ignorant of a diver's need for adaptation.
Bottom line. If something happens on the dive, you can be sure that you will be held liable by the survivors for your willful ignorance of their loved one's condition. "I don't play doctor" isn't the best defense. Trust is a two way street. If they can't trust me with sensitive information, then I can't trust them to let me know if or when it's causing them a problem.