I know many native cultures without a written language relied heavily on a tradition on passing history orally. It has always struck me as an unreliable mess.
I recognize that ultimately, all history began as oral - someone told someone something who passed it on until finally someone wrote it down. And a lot of our ancient history has a decent amount of time between the event the written version.
And all of that doesn't even consider the reliability of primary sources of the history, their biases and what they didn't understand about what they were seeing.
So really, is a written history really more reliable then an oral one?
It is a bit more complicated than a + or - reliable kind of scale.
Oral history has the distinct disadvantage that each time the story is told it often changes, sometimes imperceptibly. The slight misstatement or exaggeration from one telling snowballs to completely change the context of an event. Because the multiple versions were never written down you can't really trace changes in the story over time. With the critical comparison of written texts you can figure out when different statements were added to the text over the centuries, and sometimes even figure out who added them and why. Classic texts are constantly being culled of later additions like this.
Sometimes, however, oral histories are the best you have to go on and can contribute interesting insights you wouldn't normally get. For example, often slaves didn't write their histories, but they and their children might preserve stories that add new dimensions to circumstances that didn't leave more reliable sources. Attempts can then be made to verify the claims.
Oral history has surprised us before in regards to reliability. The Iliad was long thought to be mostly myths and Troy was often thought of as a mythical city, or at least one whose location was impossible to find. A German obsessed with ancient Greece used the Iliad as an oral history, put isolated clues together and actually found Troy in the 19th century. Other myths, like Minos and the minotaur, hide little gems pointing to the real civilizations of ancient Crete and the Mycenaeans on the mainland.
Written sources are often preferable, but oral history has made some pretty great contributions we shouldn't overlook.