I hope that makes sense!
Awesome question! I have ten minutes here so I'll answer as much as I can.
So, an oral history is part of an oral culture, i.e. it's part of an oral tradition, it's part of a language, it is part of a body of literature. That is to say, that the more you know about story A, B, C, D, you also tend to now know more about stories E, F, G, H, and also more about what someone was trying to tell you when they chose to tell story J to you the way they did, or whether the word choice was part of the story, or a choice on their part in the moment. That is to say that in general documentation if done right can be a good thing for an oral culture, but of course also presents challenges.
Here's some examples. So during the era of salvage documentation, when researchers travelled around recording the "last" of culture a, b and c, there was quite a range of skill brought to bear. Part of it comes down to how well we are aware of conventions. You would think that someone who was recording stories would get everything right, but let's say you're recording on paper, and you're writing down the basics. The problem is, what if you don't know what the basics are? Some of the early work of Franz Boas is like this - he goes through different stages where he records super accurate, where he summarizes (too much), and then maybe goes back to more accurate. Other researchers like McIlwraith (working on Nuxalk Oral History) tended to give fairly bare bones accounts of stories that while they might have been useful for recorfding history, were not useful for recording the subtext of narratives - i.e. we learn from the record that a man met a Sniniq', but we don't realize that this is a story giving the attributes of a warrior because translation and the trimming of "fluff".
So what does this mean? Basically it means that today when I record oral history, I use a tape recorder and get many versions, not because they're different necessarily, but because they might insert different "fluff" which is the actual meat and potatoes of the stories, the real reasons these stories are often being told in the first place.
Now the hard part is taking this and adapting it to ongoing oral tradition. First - where I live/work and also in my own community, people still tell lots of stories. Most stories are still alive, and if you listen they have changed a bit. Generally they have changed in that they are told with more words. More context is given, etc., but by and large the details are the same.
What has happened at times is that the social context of these stories has shifted/been lost. Because of the social upheaval of things like colonization, language destruction, residential school and such, people have a very different set of tools to bring to bear on the interpretation of a given narrative.
this means that while a story used to be understood to be a the story of a lineage, its hearers now might just think of it as a story, and while another story might have just been a story, those who listen to it now might use it as something like a just-so story. There's all kinds of changes happening, from a "legalism"ing of narratives (where you use them sort of like scripture) to some people changing stories in ways that previously might not have been acceptable.
So what to do? The real challenge is that the "original" stories were told to the "original" audience who had all of the cultural background to get what was being told. I find myself in a position where I am using oral stories to share that cultural background with young people, and because they don't have the tools I have to in many ways expand, explicate, and give big asides to a story as I tell it. It also means that I have to tell three or four stories at a time in order for the point to get across. I'm still trying to communicate the same thing, using the same story, but because the audience has changed, so must the way in which the story is presented - at least for the time being.
This type of re-packaging oral history to make it comprehensible is going on all around the world amongst colonized peoples, as we embrace our culture, but also realize that getting to our culture (rather than just fetishizing it) means taking the time to actually understand it, what its values are, what people are trying to say, how they are trying to say it, and why. If we are successful in rebuilding those values in our young people, eventually we could even go back to telling stories the way our elders did, and have the same ideas get across, and while of course we do still often tell stories like they were told to us, or like they were recording a hundred years ago, we also are embarking on the much bigger task than just learning all the stories, the task of learning and understanding all the stories, why they were told, what was being said, word choice, and all, and for this, recorded oral history, and recording oral history, both in the culture's language and in the colonizing language, becomes very useful.
I hope this has been informative.
edit: a big part of taking oral history modern is not about changing it, but maintaining it - i.e. telling modern stories. One of the big impacts of colonization has been to take away peoples' voices, so telling stories of your experiences, your family, and your community are also a really important part of ongoing oral traditions, and again, having reference to what came before can allow you to make that telling richer for you and for those you are speaking to.