Given that it's extremely difficult to eat low carb and vegan at the same time (not actually impossible) this is an interesting observation. Meats don't have carbs. People who eat meat therefore probably eat low-er carb, right?
Of course, the vegans had considerably lower BMIs- they do in every study of veg*ns compared to meat eaters (and I have looked) and I figure that probably accounts for most of the difference. I suspect a lot of the difference, maybe all of it, would disappear if you controlled for BMI. On the other hand, if a high carb diet CAUSED diabetes, then I really really don't think that the lowered BMIs would be enough to reduce the rate of diabetes so dramatically in high carb eating people. So, simply put, I DO NOT think a high carb diet causes type 2 diabetes.
That is, of course, a separate issue from whether or not a high carb diet is healthy for people who already are diabetic, and there I don't think the evidence is nearly as clear. Because there is a lot of evidence that low carb diets do not have bad health effects and do lower A1cs at least in most people who are newly diagnosed with type 2 diabetes. There's less evidence later on in the course of diabetes or in type 1 diabetes, but frankly, it does seem to be one way of making blood sugar more manageable for some people.
That said, vegetarians with type 2 diabetes tend to have better blood sugar control than the average type 2 diabetic (maybe this has to do with already being good with dietary restriction? Don't know).
It is puzzling though, that both high carb and low carb diets seem to improve diabetes control as compared to a "standard" diet, and I think the answer is hinted at by the fact that nondiabetics who go low carb even for a few days start going higher on oral glucose tolerance tests. My hypothesis is that the body can adapt to a high carb consistent diet. It can do it very well. It can also adapt to a high fat, low carb diet. It does that very well. I suspect the problem with the standard diet is that the body doesn't do as well going back and forth from high fat low carb to low fat high carb.