This is of course anecdotal, but a few years back I did the polyphasic experience, and I can confirm that dreaming consistently occurs during those 20 minute naps, which strongly suggests REM sleep. In fact, those dreams were some of the best and most vivid dreams I've ever had, presumably because you're never more than 20 minutes away from consciousness, so you remember the dreams clearly, and the dreams are strongly correlated to your mental state going into the nap.
Everyone should try the polyphasic experience for at least a few months of one's life. It radically alters the way you think about time.
To reference Dement's book again, this seems to be well established. If you deprive people of REM sleep, it will start occurring sooner and sooner after falling asleep, so that after a while the subjects would fall asleep and start dreaming almost instantly. (Which made the experiment difficult to continue since the subjects would get very angry after being repeatedly awoken immediately after falling asleep... ;-)
The first week of going polyphasic involves substantial sleep deprivation. You are basically worthless for 1-2 weeks, though you can catch up on some light reading (as I recall, I used the opportunity to dig back into PAIP...).
After a couple of weeks though, you are really refreshed by those 20 minute naps. It's rather amazing. You wake up much more alert and ready to take on the world than after any normal 5-8 hour night of sleep. And you can continue on this pattern, sleeping only 2-3 hours every day, for a seemingly indefinite amount of time, while feeling great.
That's the personal anecdote that appears (with a small and self-selected sample) to contradict your interpretation of Dement's statements.
Everyone should try the polyphasic experience for at least a few months of one's life. It radically alters the way you think about time.