When you do a juice fast a lot of the weight you lose isn't just fat. The alkaline minerals from the juice allows your body to let go of stored acid waste.
Your body stores acidic waste in your fat to protect you from it until it can neutralize it and keep it from hurting your eliminating organs.
Your body will hang onto this fat to protect you. So it is true that you could lose more fat with juice than with water.
The juice is also good nutrition and will keep your body from going into starvation mode, which slows down your metabolism.
It also keeps your body from taking minerals from your bones to neutralize acids.