Have you woken up in the middle of the night and felt healthy? I have, many times. Sometimes I sleep deep for 4 or 5 hours and wake up, and feel no pain or weakness in my legs at all. It's as if I recovered. This usually happens after a day of long walk. Then I go back to sleep and, when I wake up in the morning, I'm back to achy, weak and fatigued self all over again.
Using your muscle does tremendous damage to your body. And your body produce literally thousands of biochemicals to repair the damage. And then there is immune system response that lasts several days. Healthy people don't know it because the body automatically repairs in the background.
Sleep is probably part of that repair process. Your body may be producing different biochemicals as your sleep progress. And it's possible that, in early stage, it is suppressing whatever is irritating CFS patients, and then restore the normal state by the time you wake up. It would be interesting to draw blood every hour and see how the biochemistry changes while you sleep, like the study that tested blood every hour for 3 days after exercise.