Is there really a distinction between folklore and fakelore? The Red River Lumber Company is long gone. There is no copyright. No one can claim Paul Bunyan as their own (although I’m sure Disney will try). There is no official Paul Bunyan anthology. We know about Paul Bunyan because people hear the stories and pass those stories onto others.
Sometimes we get into idiotic purist arguments. Some of those original stories may be able to trace their origin from some hack who was trying to earn another paycheck, but I’m sure Aesop would also clear his throat and pass around the hat after he told his folk lore tales. The fact is that people hear these tales, enjoy them, and pass them on. They sometimes make up their own, or maybe confuse one tall tale with another. (“And then Paul Bunyan went on TV and said, ‘Regardless of what they say about it, we’re gonna keep Checkers’.”). Doesn’t that make them folk tales?
So what if the stories were cleaned up a wee little bit from the lumber camp version as they became children’s stories. ("Paul Bunyan and the 10,000 loose women? Maybe for the children’s book, we’ll rework that as Paul Bunyan and the 10,000 lakes"). The Brother’s Grimm’s did the same thing, and we still consider them folk tales. (“And, then Little Red Riding Hood climbed onto bed, and said to the wolf, ‘Oh my what a big… big…’, …uh…, Okay kiddies, I think we’ll just stop here and read about Mike Mulligan and his Steam Shovel.”)
The tales of Paul Bunyan are just as much folk tales as the story of Rudolph the Red Nose Reindeer (and his friend, the elf who wants to be a dentist).