Just to be clear, the reason is that we recommend strongly that people do not sleep in rest areas because there have been many cases of serious and violent crime against travelers.
Rest areas by their nature tend to be a long distance from populated areas and see relatively little patrol. On top of that, their locations right along the a freeway are an ideal target for criminals because it provides the perfect opportunity for a quick getaway. A sleeping traveler is just about a perfect target for a criminal, and putting up shades is practically an invitation that a defenseless victim is inside.
Florida now has armed guards patroling their rest area, because of the murder of several travelers a number of years ago, but almost nowhere else offers such security. There have been several other cases of robbery, rape, and arson throughout the country, and most of those cases are never solved.
I would never tempt fate just for tradition sake, especially since there are so many other options - like truck stops - where you can pull over to sleep, in a much safer environment.