If you have a healthy metabolism, and you eat a high carb, low fat diet for a few days, your body will adapt, and you'll be more insulin sensitive due to adaptations to better utilize glucose. Go on a fast or a low carb diet for a few days, and you'll be less insulin sensitive, because your body has set itself up to spare glucose. These transient changes in insulin sensitivity are interesting enough, but type II diabetes doesn't happen suddenly, it develops over the course of years. And once it has developed--going on a high carb, low fat diet may or may not be an option. It doesn't matter to your body's cells whether the fat that's competing with glucose for uptake comes from the diet, or the body's own fat stores.

A fellow named Kempner developed a Rice Diet that he used for various diseases, one of them type II diabetes. The diet consisted of rice, fruit, and white sugar. An important caveat here is that while for lean patients the diet was unrestricted, for overweight patients (where most of his type II patients likely fell) he restricted the calories--I believe it was about a thousand calories a day. Later on in his career, it made the papers that he actually whipped some of his patients, at their request, to get them to stay on the diet.

Also, even if it works, and without the whips, so, often, does a low carb diet. A low fat vegan doctor may claim that type II's can't eat any fat, or they'll be glucose intolerant. But here's the thing--a type II diabetic who eats glucose may exhibit elevated triglycerides and other lipid abnormalities. It makes as much sense to say that dietary glucose has made them fat intolerant as it would to say that dietary fat has made them glucose intolerant. Choose your intolerance, I guess. If you can. Too many diabetics do just fine on a low carb diet for anything approaching the blanket disapproval of the forks over knives people.