OK let's ignore protein for a second. You're saying that if you eat the same number of calories, but as fat instead of carbs, your body will store less of it. i.e. that the human body is much more efficient at extracting energy from carbohydrates than it is from dietary fat, i.e. more of the energy from dietary fat is wasted. Macronutrient choice cannot affect the amount of work that your body does, only what percentage of the calories are wasted (inefficiency).

On the face of it this makes no sense because fat is such a good energy source that it's what our bodies use to store energy, so why would our bodies have problems extracting energy from dietary fat?