It's hard to believe a story can persist for 15,000 years by verbal transmission.
It's like the psychic who correctly predicted the last 7 presidential elections. One doesn't hear about the other psychics whose predictions didn't pan out.
The Klamath Native American tribe has legends of the eruption of Mt. Mazama that formed Oregon's Crater Lake - which happened in ~5677 BC [1]. If oral legends that reflect real events can last seven and a half thousand years, is there any reason to think they couldn't last 15ky, or 20ky? It seems to me all that's needed is a continuous cultural line.