Technically not true. If you go into ketosis, you end up burning ketones instead. It's hard, but possible.
Unused Sugar is turned into fat which is broken down by the liver into ketones. So you don’t get ketones without sugar
I'll defer to you, as I don't really know, but if one were only eating fat and protein, so taking in almost no carbs to be broken down into sugar, wouldn't you be skipping the sugar step?
Protein is still being broken down into sugar, but it takes much longer than carbohydrates, so you feel fuller longer and it is not as taxing on the body. That’s why you cannot overeat on a protein diet.