I remember when this book came out. I think the tips are misleading. For example, I guess if you have a distended belly due to gas, then this drink will help relieve the gas - and cause you to drop a couple of pounds of water weight from the diuretic effect of the ingredients. Your belly may go down temporarily. Water + Gas does not equal fat.
If you normally drink beverages with calories, such as soda (which is prohibited on this plan), and drink this mixture instead then you'll probably lose fat as well. But it's not the sassy drink causing the fat loss, it's the reduction of calories from the foods you eliminated.