I don't know about the song "Dan Payton's Ride" but I do know that the story about his ride was soundly discredited within several weeks of the flood. The newspapers of the day, reveling in the sensational nature of the flood story (and the increased circulation it brought them), did very little fact-checking and spread this heart-warming and inspiring story to many eager readers.
However, parts of the story did not make sense to the locals (like how can you gallop in 1 to 3 feet of water?) and it was investigated, found wanting (even to his name: no Daniel Payton was known in the entire valley. Although a family of Paytons perished in the flood, Dan was not one of them), and deemed a part of the flood mythology.