Sugar is not fat. It's completely different from fat. Sugar is used by the body as energy. Any of that energy that isn't used is converted into fat by the body for use later. But sugar itself is not fat.
Sugar is carbohydrate. Carbs are an easily accessible energy source, but if you don't access them, the some of the left-overs will deposit as fat (through a long, boring process). So yes, its a bit of a fallacy that some fat free products are really all that healthy. Eating them and taking some exercise is better than eating very fatty foods and exercising however.