Yes, sugar isn't the culprit in diabetes, fats seem to be most problematic (described rather in detail in the scholarly report at
Causes of Diabetes mellitus: Does Garcinia Cambogia Extract Increase the Risk of Diabetes? ).
But you should focus on getting carbs from fresh fruits and fruit juices instead of starch from "bread, potatoes and crackers" to increase your metabolism and counteract the diabetic state.