Fat people get hungry despite being fat because the machinery of metabolism and satiety is broken. The exact mechanism is subject to debate, but most of us agree that there's an element of resistance (whether built-up or caused otherwise) to the hormones that regulate appetite and satiety. To name a few (and I'm not a biochem guy, so more educated persons can add to/correct the list), Leptin, Insulin, Glucagon, Ghrelin.
I always say the reason this works for weight loss is that it allows that machinery to function as it was designed. Also something that is hotly debated and disputed here from time to time.