It's not ok to eat lots of cheese because it does have carbs. But the idea on a low carb diet is to count carbs and not worry about the fat. Your body burns carbs first (converting them into fat if you eat too much), then bodily fat. For some reason (Dr. Atkins explains this) your body burns bodily fat before dietary fat.
Personally, I never bought into the concept, and I follow a diet that is low carb and relatively low fat.
Hmmm, Lil_G, I never thought about the caffeine thing. I've just found a justification for my coffee habit!!