Also, there is absolutely no reason for a diabetic to avoid fat intake.
Doctors tell you that so you avoid overall energy intake, because they think you will get heart disease if you become fat. We now know that the cause effect realtionship is all wrong here, and all, but anyways... my point is, someone with diabetes can eat fat just like anyone else (40% of total energy intake). Low-carb AND low-fat diet is just low-energy diet. As long as the blood glucose level and caloric intake are under control diabetics don't get fat.
No point in reducing fat intake, if not detrimental...