For a study to be valid and useful, the control group has to go through exactly the same criteria as the test group. Everyone is "blind" to whether they get the placebo or the real thing. So they all get the same interviews/tests and rejection criteria. Putting all the diabetics in the control/placebo group would make it pretty obvious who was and wasn't getting the real thing.
Even if it isn't blinded, you try to make sure the control group and experimental group are equally representative though, you don't "put all the X in the Y group" ever, this is true! Because the whole point is testing two groups as much alike as possible other than the thing you are testing.
