Diabetics CAN eat anything they want. Including sugar and sweets and sugars and ice cream. However, they must eat those in limited quantities. Sugar isn't the only problem - it's all carbohydrates - potatoes, peas, beans, bread, pasta, apples, bananas...
Most diabetics should restrict their carb intake to 45-60 grams per meal. Some people can eat more, some less. It all depends on the individuals ability to regulate their blood glucose
Since all carbs cause the same rise in bg, the difference is trying to eat carbs that are high in nutrition, like the bananas and peas, and skip the carbs that have little or no nutritional value - like syrup and soda.
Milli: There are more than two types of diabetics and none of them have anything to do with the production of sugar. It has to do with insulin
and the body's ability to either utilize it or produce it. Type I don't produce enough insulin, and Type II produce plenty of insulin, it's just that their cells are unable to use it to break down glucose.