I assume we are talking about Type 2 diabetes.
Fat in the diet is not the main culprit as far as build up of fat in and around the body is concerned. Carbohydrates are what make you fat and put fat around your organs. Carbs do this by stimulating insulin production (the fat building hormone). In a T2 diabetic, the insulin is now longer processing the carbs correctly, so there is a build up of both insulin and sugar in the blood and around the body - this is bad news. Many people have found that avoiding carbs avoids the problem.
Fat does not create problems for the typical diabetic and, arguably is the way, as human animals, that we should be getting most of our energy, not via carbs and sugars.
Sally