The Claim: Certain foods cause you to burn more calories digesting them than others
Protein actually has a slightly higher thermic effect than carbs or fat. In other words it takes a bit more energy to digest and metabolize protein. But this effect is minimal and will never help you actually lose body fat.
The thermic effect of protein might add up to at most 10% of the food eaten. In other words, it would be eating 1000 calories in order to burn 100. This is a pointless road to travel if your goal is fat loss.
Just eat less total calories to burn fat, and don’t bother concerning yourself with the composition of those calories.