I don't know the mechanics, but my understanding is that such a water fast also permanently alters your digestion and metabolism.

A (logical extreme) example I was thinking of counterig with: if you eat 500,000 calories in 24 hours on the first of the year, and nothing else for the rest of it, you'll achieve a 1,350 calorie/day average, certainly enough to lose a significant amount of weight. And you will! Because your stomach will have ruptured and you'll be dead by the 2nd. Rotting is one way to burn calories. (I mention this to illustrate how focusing solely on the numbers, to the detriment of the actual lived quality of life during the weight management process, misses the forest for the trees.)