While you're right that fat in and of itself does not lead to weight gain, it's the combination with sugar that absolutely, 100% leads to weight gain. Sugar and other high glycemic index foods (eg white bread) causes an insulin spike and puts your body into an anabolic, "building" state in which it will assimilate whatever it has lying around. Usually, if you're eating something with high amounts of sugar, it will also have high amounts of fat (ice cream, cookies, etc). Thus you will have a large amount of fatty acids lying around which your body will go ahead and form into droplets to be stored in adipose tissue. That's how you build fat.

However, if you are in a state of muscular stress, such as after weight lifting, and you eat a ton of glucose - notice I said glucose, not sugar, which contains fructose - and you combine this with a moderate amount of protein and little to no fat, you'll have a bunch of amino acids floating around and this insulin spike will cause your muscles to soak up all that protein and become bigger/stronger/both depending on the type of weightlifting you did with no spillover into adipose fat tissue.

It's this very simple metabolic process that people don't get. Everyone gets all worked up on pointing the finger at fat or sugar or whatever, but this is the "secret".

Btw, for anyone looking to lose weight or put on muscle in a healthy way, check out intermittent fasting, specifically the leangains plan.

Source: I'm a biochem major with a six pack