misconception about sleep cycles with naps?

In a different thread I asked a question as to why people are entered directly into the REM phase of sleep when taking daytime naps. Then I recalled, I had never heard of this phenomenon until arriving at this forum… I did a little research, and realized there hasn’t actually been any scientific claims to make this evident. In fact, everything I found indicates that you start the nap in stage N1 sleep, just like at your regular nocturnal sleep schedule. As an easy way to describe it, short ones are often called “power naps” (coined by cornell university social psychologist James Mass) for this very reason. You enter stage 1, proceed to stage 2, and terminate before stage 3 deep slow-wave sleep so you do not develope sleep inertia and awake groggy. So my question is, where did this claim of instant REM come from, and what exactly backs it up as fact?

Edit: I changed the topic title to be more accurate and informative about the post.