I like your theory, but it doesn't line-up with my experiences. I started to document my dreams when I was a teen (a long time ago). Over the years I've become a halfway "ok" lucid dreamer. If I wake up from a dream, I'm pretty certain as to if it was a REM sleep dream, or light sleep dream. Even without lucid dreaming, if you keep a pen/paper by your bed and start to write down your experiences, you'll be AMAZED at how much you really can and do remember your dreams.
Anyway, I have the "can't punch" or "can't run" situations in dreams too, and largely they're in full-on, big and bright technicolor REM sleep dreams. The opposite is true as well, in that the fun, totally cool-awesome dreams are usually in full on REM sleep as well. My favorite dreams are my flying dreams. They start a bit different, but most always end up with me being able to fly, and control that flight. They're even more fun than sex dreams, because as I've become a bit lucid in dreams - sex dreams can be frustrating, as I never get to really finish those dreams.