Insulin plays a role in regulating the patitioning of fatty acids in the body. The flawed thinking, that calories burned by the body is a fixed amount that doesn't vary based on calories consumed, is simply wrong. The key is that energy expenditures only rise when the calories consumed are not being partitioned for storage. Elevated insulin levels cause storage of fatty acids, and inhibit release of fatty acids from fat cells by triggering them to be bound up into triglyceride molecules.
I'm not some hardcore paleo/keto/Atkins dude, but reducing carbohydrate intake (particularly refined carbs) makes appetite control much easier, by virtue of several obvous and not so obvious reasons. The obvous is that proteins and fats fill you up more (satiety), and that could be accomplished with diets that aren't high in fat by simply upping protein intake, of course. However, the less obvious is the energy partitioning going on with low insulin levels. The fat cells are behaving as they naturally should, pulling in and releasing fatty acids in a balanced manner.