Earlier quoted context omitted.
I don't think that's the mechanism. A caloric deficit causes your system to metabolize whatever it can. It likes fat because that's energy dense, but muscle is also a good source of energy as well, and the more rapid the weight loss, the more body mass it has to burn.
As far as I know, muscle is only used when fat reserves are depleted or you don't eat enough protein for the brain's personal amino acid supply. I'm not particularly knowledgeable about this, though, maybe an expert can weigh in.
Secondary to that, the body needs some amount of glucose. The best option for that is stored glycogen. When those stores run out the body can enter ketosis which reduces but does not eliminate the need for glucose. Fat consists of three fatty acids joined by a glycerol part. Most of the energy is in the fatty acids, but the glycerol can serve as a limited supply of glucose. However that is not really sufficient, so to get more glucose, and the other option is breaking down protein.