Hi Tracy,
I can understand exactly what your nurse was trying to tell you, but unfortunately she doesn't seem to have made it very clear.
When you are overweight, the fat layer, particularly round the middle of the body, makes it difficult for the body's insulin to metabolise (i.e. process) blood sugar. This results in high blood sugars, an over-production of insulin, and even more fat accumulating. By reducing your own body fat (not fat that you eat) you reduce this insulin resistance and your insulin can process the sugar easier.
Where does body fat come from? All carbohydrate that you eat is converted to blood sugar. Your body produces insulin to process this by storing the sugar in your body's cells. It first tries the muscle cells and if these are full, it tries the fat cells. If these are also full then the insulin creates new fat cells to store the sugar in. This is how body fat is made. If you think about it, how do farmers fatten cattle up for market? The feed them on a high grain (carbohydrate) diet! So the way to stop more body fat from being created is to eat less carbohydrates. By eating a lot less carbohydrates not only will your body not build new fat cells, but it will burn off the existing ones and you will lose weight.
So where does low-fat come into this? Simple answer is it doesn't. Fat doesn't make you fat and nor does it have any effect on your blood sugar. What fat does do, but only when eaten with high amounts of carbs, is to become stored in your blood as triglycerides, which can block your arteries and lead to heart disease. Fat eaten with low levels of carbs has been shown not to cause heart damage.
So the answer to both losing weight and reducing your blood sugar is to reduce the amount of carbs in your diet. This doesn't mean you have to give up good food. Like many of us on the forum I eat a reduced carb diet, and I would say I have never eaten better or more healthily, or felt fitter. The easiest way to start the process is to reduce the types of foods that do the worst damage. These are the starches - bread, cereals, pasta, rice and potatoes are the worst culprits. If you start by cutting out 50% of these then you will see an enormous difference. Make up the shortfall with larger portions of meat and other vegetables (i.e. the tastier parts of the meal!).