Strelok, I agree that muscle and fat are two different things, but they are interconvertible.
Protein turnover in the body is actually 24% of the body's daily energy expenditure. As this protein is turned over, if you're not exercising, a small portion of is it burned or converted to sugar or fat through the TCA cycle. That is not to say that your muscle becomes fatty, but that the breakdown products of losing muscle mass have many fates in the body. It may not be a significant contribution, but it can happen.