I don't think you have a very good understanding of how oral history works if you think it's all a game of Telephone.As for your insistence on the total veracity of oral tradition: Have you ever played Telephone? That's how oral tradition works, with the added problem that the message will not only be distorted by mishearing and misremembering, it will be distorted because as time goes on and you learn other things you will mix new and old information up. Unless you're historians are not really human but some rare breed of half-human/half-computer they will forget, misremember and mix up stories. All it takes is for one "Historian" somewhere to want to paint their tribe in a better light, or be influenced by something they read a decade ago about the depravity of the Conquistadors and suddenly it is all wrong, no better then any other historical fiction. And you will never know, because you can never go back to read what the historians before them knew. That you somehow think these, in scientific terms, utterly unreliable anecdotes are more legit then archaeological findings, written first hand accounts and the composite knowledge of those two is utterly perplexing.
Firstly, oral history is structured. Poetry began as oral histories and storytelling; meter, rhyme, alliteration, all were mnemonic tools to aid memorization. Take modern pop songs. Part of what makes them so memorable and easy to digest are couplet rhymes and a simple ABABCA stanza structure. If you're rendition of a song is wrong, you know it, and so does everybody listening to it. Even substitions are difficult: for instance, at the end of a couplet, try substituting "bad" for "evil". Neither the rhyme nor rhythm fits. Doesn't work.
Next, there are a few exceptional/strange people able to remember and calculate things like computers. It is true that they're too few for a culture to rely on having each generation. But it doesn't take a computer to learn oral history. You have people, chosen in youth, with strong affinities for stories and excellent memories. Their apprenticeship is a full time job, for years and years. Hundreds upon hundreds of repititions, of each story, reinforced with beatings and social pressure on mistakes. It's not "a game of Telephone."
Next, oral histories are vague, yet evocative. You don't have "on the twenty-second day of the third month of the one thousandth year, 6,242 of our tribe did battle with a neighboring tribe, with 80 deaths, 754 cripplings, and 1285 wounded. We won 238 prisoners and 431 pounds of leathers." Of course that would get messed up over generations, that's not easy for human minds to remember. What human minds are much better at remembering are evocative details; something along the lines of "Many moons ago, when the flowers were blooming after winter's frost, our people met theirs in battle; through our heroism and the blessings of our ancestors, our losses were few. We put our enemy to flight, winning the coverings that would warm us through the next frost." Or, you know, whatever. It's vague, but it tells the story of the event as well as it needs to; hard numbers in history really are only particularly useful for data analytics. Relative data (this story happened before that one, it occurred somewhere thataways, it happened for this reason) is all that most people need out of history.
Lastly, an example. Historians are only now starting to recognize some of the amazing things that preserved oral histories were capable of. I've been looking into the Dreaming of Aboriginal Australians. Not only is it a collective set of myths and history for a continent, it is the most amazing geographic information system I have ever rncountered. There are songs/stories called songlines: part mythic, perhaps partly historic, but through reciting them Aboriginals were able to guide themselves along landmarks across routes that went through the whole continent. The big kicker: Aboriginals from one end of the continent seem to have been able to navigate through territory they had never encountered through a relevant songline, even if the area was one that nobody from their tribe had ventured to for hundreds of years, and even if the local Aboriginals spoke a wholely different language than the traveling ones. This oral geographic system was passed down for tens of thousands of years SUCCESSFULLY, and modern Aboriginals who have been successfully trained in their people's songlines can still navigate across Australia with them... provided the key landmarks have not been destroyed in colonial expansion.
Like, this is a phenomenon that has been observed and documented. As a student of geography, it ranks as one of the most incredible things I've ever heard. It got me to look into the veracity of oral histories. I'm giving L'il's, and by extension other Native Americans, the benefit of the doubt. Humans are amazingly adaptable creatures, and that another culture went along another route of innovation does not discount their achievement. Quite possibly, their past is better documented in their oral histories than ours is, piecing together what we can from shattered tablets in Mesopotamia.