That might be so.I don’t have much to offer except that robust oral traditions lose nearly zero information in their transmission, and drawing from all the peoples of the world it would not be unreasonable that an oral history or two made it thousands of years unimpeded.
We know that within our historical record spoken language has changed pretty dramatically over short periods of time (hundreds of years) and even more so since the first cities were built. I do not think that any oral tradition begun in one language could be continued and be intelligible over 1000 years, let alone 10,000. A single story strand over such a time line is unlikely and multiple strands would end up with thousands of variants over time. In addition, given the small tribal nature of life 4000-10,000 years ago, the likelihood of any storyteller and his descendants living in some unbroken chain is pretty low. 10,000 years is a very long time. It is over twice the length of our written history. Conjecturing such a thing is fine, but it is too easy to say that a modern oral tradition that says "the land flooded and we moved inland many moons ago" means 1000 years. It reminds me of of how folks read the Books of the Prophets in the Bible and interpret them to fit current events. It's just making the story fit the outcome you want.
Some real life examples of very long oral traditions would be nice. Seeing the myth that Berzerker is talking about would be helpful