I believe this is not "that" accurate. Generally the presence of excess carbohydrates cause the body to prioritize sucrose/fructose/glucose to glycogen conversion and storage & usage. Dietary Lipids that are ingested are stored rather than used for energy. While, De novo lipogenesis (turning carbs to lipids) does occur, it is inefficient enough that the body barely converts something around 1% of carbs to fat.
Since glycogen is stored in the liver and muscles, and insulin signals the muscles & liver to take up the glycogen in the blood, this is probably where diabetes starts when the liver and muscles are already filled with enough glycogen and there is no where for the glycogen in the bloodstream to go.
If the body could efficiently convert sugars to lipids, I don't think diabetes would be that much of an issue. People would just get obese with the diabetes.
AFAIK, the priorities for energy consumption of the body is:
1. sugars into glycogen into ATP
2. protein into glucose into glycogen (gluconeogenesis) into ATP (some limited amount)
3. lipids into ketone bodies into ATP
So as long as the body was sugars to use up, that is the priority of usage.
One of the most calorically intensive tasks the body does is growth and repair of new tissue. Excess sugars are generally used up by kids who are growing. However, once people reach adulthood, the growth rate slows so significantly that the excess caloric intake forces all the lipids ingested to be stored.