Word of mouth was likely valued differently than it is by us. We may look down on it, but word of mouth was/is the trusted means of passing on knowledge for many cultures, even when writing was an option. And it can be accurate through the ages.

Aboriginals in Tasmania have oral traditions dating back to when it was connected to Australia. 12,000 years ago. Or oral records of hunting grounds dating back to the Ice Age that are now under water.

Both Achilles and Odysseus have had their own religious devotions through the ages. And whether you believe or not, they're still a bit different than something that was published explicitly as fiction.