No, fats are most likely not the problem, It is much more likely that sugars are.
While it is true that the same amount of calories lead pretty much to the same storage of fat, this fact is irrelevant.
I think that the question that we should ask ourselves is why we eat more calories than necessary, and the answer is not necessary a psychological one, or one that needs to invoke the nebulous concept of willpower.
Intake of sugar (most pronounced with rapid absorption of sugars) leads to high blood sugar concentration, which will need to lead to an insulin response to counteract it. The secretion of insulin will make you end up with a lower blood sugar as before the meal, which will lead to a higher appetite.
Isocalorically, fat will not lead to such a pronounced curve, so you can extend the times between meals. There is no physiological need to eat food every few hours, as you might have been told.
Sugary foodstuffs are also typically binge-foods, like ice-cream, cookies, milkshakes, soda, crisps, fries, or pizza. (I am aware that some of this foodstuffs also contain fats, but my argument is that stuffs high in fat, but low in carbohydrates aren't typical binge-foods).
Additionally, most consumed carbohydrates are empty calories that are, opposed to fats, not necessary.
Low-Fat diets have no positive effects on cardiovascular mortality, so there is no reason not to eat a moderate fat, very low sugar diet, and decrease the physiological effects of overeating.