I have read this before. I do not understand how you can sleep for 20 minutes. It takes more than 15 minutes just to fall asleep.
There are many stages of sleep; stage 1 through 4, and REM sleep. These, it is hypothesized, have distinct physiological functions. Most importantly for this discussion, waking up out of each have very different effects.
Waking from stage 1 sleep makes you feel immediately refreshed, and people perform better immediately have tests of mental acuity. This is also true of REM sleep; additionally you often remember dreams.
Stage 2 is also good. A good 30 minutes afterwards, you will feel better rested, and your mental acuity will rise; for longer than from stage 1, but it is a delayed effect.
But if you wake up out of a deeper sleep cycle, you get 'sleep inertia.' Mental acuity plummets. You feel poorly rested and ill.
The problem:
The body is often not even aware that you are sleeping in stage 1 sleep. You are in a different physiological stage, but you may not have lost consciousness.
You usually are in this stage from minute 5 onto minute 10. And in stage two up to about 15-20 minutes. After that, you can fall into a deeper sleep; which waking up from is very problematic.
I used to set my alarm for 30 minutes. I'd way up, feel even more tired, and set my alarm for 30 minutes again. This was ruining my life.
---
tl;dr
Even if you don't lose consciousness, you can still be 'sleeping' and a nap of 20 minutes will greatly help you feel healthy and well rested.