[twoslide]

You are right that your body can burn muscle as well as fat. However, decreases to energy consumption ("metabolism") are minimal. Our bodies are evolved to use energy efficiently, if it were possible to do everything we do (or even some semblance of it), with far lower energy consumption, we'd already be doing it.

A good analogy might be fuel consumption in a car. Some savings can be made through efficient driving techniques, but ultimately there is a core amount of energy needed to transport the car across a given distance.