Yes!
Very simple, if I burn X amount of calories daily all I need to do is cut calories to an amount less than X to lose fat.
How can you even argue with that? 
because it isnt that simple.
you will lose weight- not all of it will be fat, and the body leaves fat burning to the very last resort, so any initial loss will not be mostly fat.
however a calorie isnt a calorie as the body will spare what it can depending on the nutrient balance that it is currently in.
So if you have a high fat diet- i..e little carbs and little protein then a calorific deficit will burn fat, but it will not burn all the fat you're taking in, as it tends to store that. It will however not be able to replenish the existing carbs and proteins in your system so will instead result in burnt fat, and burnt carbs/protein.
since you're on low protein and carbs, then you will actually lose size and energy, resulting in a lower metabolism and even less fat burning, and more fat absorption.
on the other hand if you have a low fat diet, your body will preferentially burn proteins and carbs in an effort to store the fats. If you have a calorific deficit, you will burn those nutrients as well as some fats, but since you're on a low fat diet, you will actually end up reducing your fat stores over time, but yes you will burn the good calories. The difference is that by burning less fat, your metabolism will stay active as it requires more digestive action to break down the lower energy nutrients so thus will continue to burn more efficiently.
so although it is true that you will lose fat with a colorific deficit, you may actually be inputting more fat to replace it, and actually slowing your metabolism.
the thing that eveyrone has forgotten is also that this does not work as a static regimen.
the body again adapts to make use of the nutrient composition it is receiving. if it gets high protein then after a few weeks, it burns lots of protein as it attempts to find a balance. same for carbs, and not quite the same for fat- fat is actually stored as part of our survival mechanism. a high fat diet burns fat after a while, but also stores alot of it.
thats why a calorie isnt a calorie.
and thats why some skinny people have high fat %.
