Why are people with diabetes told to consume less fat in their diet?

A. There are two reasons why people with diabetes are typically recommended a low fat diet - one, increased fat in the body interferes with glucose uptake by the cells. Thus, lower fat levels in the body help manage blood glucose levels more effectively. Secondly, certain kinds of fat are deposited in the arteries, leading to plaque, thus leading to heart disease and hypertension - the single biggest risk of death in people with diabetes. Diabetics are more prone to the formation of arterial plaque and hence, need to consume less fat.
However, do remember, a low-fat diet does not necessarily mean a high-carb diet.