There are two things that come to mind when we ask if dietary fat causes obesity. First: fat and carbohydrates sum to
literally all of food. The caloric value of protein is (essentially) negligible. What is certainly the case is that we can point to people who are fat (preferred term) on a low-fat diet. We can point to people who are fat on a fat-intermediate diet (rough balance of fat/carbs). Can we find many people who are fat on a low-carb diet?
I suggest that if we do, most such people will not be found eating fat in its natural form, but as rendered fat and pressed oil. It is almost certainly the case that the way in which fat is consumed affects satiety: the body cannot see a caloric benefit from fat until it is beta-oxidized in the liver, many hours after it is consumed. So in order to estimate how much you have eaten, the body assumes you have consumed fats in their natural form.
This is key to most low-carb diets: fat is usually consumed in its natural form, since nobody drinks oil (eww) and fatty snacks such as potato chips are banned. It is also an intrinsic feature of the "paleo" diets, which ban processed foods.
So, it might not be too much of a stretch to say that fat as a naturally occuring part of foods like almonds does not make us fat.
The second thing that comes to mind is the balance of omega-6 and omega-3 fatty acids in a healthy diet. When this is tilted excessively in favor of omega-6, the body produces an excess of certain endocannabinoids (arachidonic acid) which contribute to overeating:
http://www.sciencedaily.com/releases/2010/07/100726221737.ht...
[NB: the mechanism is up in the air. The effect is real.]
The additional, final consideration is the alleged link (as stated in the article) between consumption of land meats and obesity. See https://en.wikipedia.org/wiki/Red_meat#Obesity
I've been harping on "natural", and meat is natural, so what gives? Weirder yet, the correlation is with meat protein, not with fats. And we do know, though, that people on e.g. ketogenic diets lose weight while eating lots of meat: http://ajcn.nutrition.org/content/82/1/1.short
The simplest way to assign blame is to cry confounding: while meat itself is natural, it is rarely consumed in a natural-food context. Instead, since meat is culturally considered unhealthy, it is often eaten on white bread or in a pack of Lunchables. Support for the confounding hypothesis would be a low r-value in studies that link meat consumption to body fat (i.e. total variation in body fat is only weakly related to variation in meat consumption); falsification might be a very high r-value, or a very well-controlled study.
[NB: I believe the confounding hypothesis.]