Like I said, I'm just restating what I read in Dement's book, which hasn't talked about this technique at all except to say that people who wake up frequently (like people with sleep apnea) are much more tired than they should be, because the awakenings actually don't change the total amount of sleep that much. So there seems to be evidence indicating that many short chunks of sleep are less effective at reducing sleep debt than one chunk of the same total length. It's as if there's a "startup cost" to falling asleep, and it doesn't start to benefit you until after some time has passed.
So I should have formulated myself more carefully by saying: Studies indicate that short periods of sleep is less effective than long ones, and that each individual requires a certain amount of sleep per night (but which varies with individual and then as you age).
He did go so far as to say something about how he thought methods advocating that you can train yourself to sleep less are "dangerous", given how much sleep deprivation affects your health and ability to do things like drive or operate other machinery safely.