Alright, please don't other people take my advice on this... I'm just giving my personal experience.
Whenever I'm in a rut, I kid you not I eat something that's way off my diet and I lose weight within a few days. When I was on Atkins, one day a week I would eat pizza (shh, like half of a medium one), and 2 days later I dropped weight.
I've never read anything about this... I've had personal trainers say to have a cheat meal but for the reason of not depriving yourself. Weight watchers allots weekly flex points for this as well.
HOWEVER... I swear to god, it wasn't a deprivation thing. My fiance is the same way now (I don't cheat very much now at all, maybe I should... I dunno) whenever he has some super cruddy cheat day, he drops weight a few days later.
My mom and I THEORIZED that it basically puts your body in shock. Maybe makes it go into overdrive? It throws your body completely off... I guess kinda like when you exercise the same way every day your body gets used to it? Same thing with food?
Some people also do this as carb cycling. Same principle, but within healthier parameters.