GPs claim was that non-aspartame sweeteners cause insulin to rise, not blood-sugar. This would cause non-diabetics to become hypoglycemic, and over a long-term could cause type 2 diabetes.
I always assumed that when I taste something sweet, my body starts putting insulin in my blood. Over time it learns how much to put in based on how sweet the food tasted. If that's true, I'd expect too much insulin for food with aspartame, BUT ALSO too little when food has real sugar, because of the long term learning.
I'd expect a type 1 diabetic not to see either effect because the system that aspartame wacks out of tune is turned off for them.
I appreciate that I have no actual knowledge on the subject, except that I know the body must have control loops for this stuff and they must be kept in calibration by some mechanism. Probably my model is too simple.