When ancient man recorded the events in the Bible, Epic of Gilgamesh and other ancient texts ...?

I don't think they thought in those categories. I suspect it was more like "our stories v. their stories," based on the way the Jewish creation stories respond to the older sumerian/babylonian stories. To have a story was like a declaration of sovereignty, the same way that having the ability to write a constitution is a declaration of sovereignty of a country today.