I have seen some of the post saying Fat/Oil is good for Diabetics. My personal experience is reducing Fat in food reduces the medicine intact you have to take.
As per experts Insulin just not control the sugar but also needed for metabolizam of fats. So taking excess fat will result more consumption of insulin and undigested fat in your body.
Balanced Carbs + Protein + Fiber (Veg) and least amount of Fat will give you good result.