Different strokes.....The weight lifting coaches that I work with preach getting protien into your system 45 minutes before training, having a shake within half hour to 45 minutes after and then another source of protein as well.
I could be completely wrong, but it has worked for me. Or seems to. Nothing to do with your body eating your muscles. Everything to do with giving the body the fuel that it needs to perform. Again, just what I have experienced. If you find that training while in midst of a fast work for you, then keep going.
There is some truth to the body eating muscles. I learned it from the magazine Bro's Health.
Just kidding. When the body is requested to do explosive exercise like lifting, the body taps the creatine and glycogen stored in muscle and glucose in blood that were produced from food. Short intense exercises like lifting use your anaerobic energy system, which is glycogen. Long continuous exercise like running use aerobic energy, i.e., oxygen and fatty acids from blood.
So if you intake protein before exercise, you might have built up some extra stores. If you don't intake, you probably still have enough stores if you hadn't done anything super physical earlier.
When you're new, you find yourself struggling and gasping. Your body is tapping your anaerobic system. As you exercise more regularly, your body becomes more efficient in switching from anaerobic to aerobic. The body taps into oxygen earlier, and your endurance improves. That's why marathon runners can go on forever. Their tapping oxygen and stored carbohydrates.