Oxidation of fat creates waste products. You need water to help flush them. The reaction that uses fat for fuel also involves water, so if you are dehydrated, there is a chance you won't burn as much fat. When you train, you deplete your muscles of glycogen.
The only way for glycogen to get back into the muscle is through glucose bound to water, so without enough water, you won't get the fuel to your muscles that need it. Water is what the body uses to manipulate the charge inside and outside of the cell to drive nutrients and and waste products out.
Without water, you are potentially not delivering the nutrients your body needs to burn fat.