This is not true at all. There's perhaps a preference toward fat but muscle wasting absolutely occurs during fasting, and often at a relatively significant rate.

If you were to "run out of fat" entirely, you'd simply die with fairly significant caloric reserves in the form of muscle. This is not what is observed.

This is very much not true; I lost over 100lbs and saw the evidence in myself, before I adjusted and started eating a high protein low calorie diet. If you don't consume protein and don't work out, you will lose muscle mass, even if you have fat to burn. This is because muscle tissue is expensive to maintain; the body tends to reduce it if it's not being used.

your body is constantly using protein to maintain your muscle. When you starve your body of protein, you lose the ability to maintain your muscle, and your body begins to lose muscle as well, even though it does a bunch of stuff to try to stave that off.

I also tried water fasting. Lost both fat and muscle (and I still have plenty of fat)