I'm the same. These guys say 20 minutes is the best, but in that case I think we need to choose a better term than "nap", because I won't be asleep for almost any of that 20 minutes. Rest, perhaps.
I thought I was one of those people too... every time I try to nap it seems to end up with me just lying down and trying to fall asleep for 20 minutes. However, after moving in with my girlfriend she has confirmed that I do indeed manage to fall totally asleep during these attempted naps.
I did some looking around and apparently earlier sleep stages can easily be confused for being awake, especially for light sleepers. It may sound weird, but sleep perception is a funny thing. Some people nap quite easily, yet conclude they did not sleep at all because they never perceive themselves falling asleep or waking up.
You are probably napping for too long. 20 minutes is best because you are not hitting deep sleep and may catch some REM (20 mins is also not incidentally the polyphasic sleep prescription).