I learned the same thing in EMS. I worked my day regular day job and worked on the ambulance at night. I found that even if I never really went to sleep, but just laid quietly in a dark room for a couple fitful hours of occasional dozing, I felt better the next day than if I kept on my feet all night. This was true even if "staying awake" was just watching TV, not running tough calls.

There was a definite, repeatable difference.