I don't worry about the fat in meat, dairy products, fish or olive oil. Some of it is actually good for you. However, when you cut out all your unnecesary carbs you're going to need the fats and oils to avoid the problems that arise when you consume more than 40% of your caloric intake as protein.
Your basic hunter/gatherer diet of meat, nuts, fish and roots is probably still your best bet.
They mostly starved, but you're probably right. Do you really make pizza with Provolone? I know it's a free country (sort of), but some things just aren't right.