Personally, I need to remind myself not to confuse the music industry definition of folk with the historic definition of folk. We all know that, originally, folk was not this genre or that genre. It was just the (mostly) non-commercial sounds of some race, some region, some occupation. The sound could have been anything--ballads, blues, gospel.
So why not rap? I'm no rap expert but I think at least initially the whole culture was pretty much of the street, with an older heritage as several people here point out. As I see it, the confusion about "Folk or not?" stems largely from the fact that the music industry machine is so voracious today. It notices a great deal and if it senses some commercial potential in a sound it'll glom on to it--then discard it if it doesn't work fast, or make a billion bucks if it does. I guess that didn't happen quite so quickly in 1900.