It is also true that when we crave and binge due to a nutritional deficiency, the things we crave and eat often are unrelated to the real deficiency, or too low in that nutrient to alleviate the problem. What it is we end up craving is affected by, as you are aware, the foods we have on hand. But it is also determined by our perception of what our body needs, as well as what we permit ourselves to crave.
So people who are trying to follow a fat-free diet may binge on bag after bag of fat-free candy and box after box of fat-free cookies, because they see these as acceptable options. They push the obvious to the back of their mind, because they can't accept that it is fat they need, and the carbs are a trigger for them to eat even more carbs.