In order to answer questions about the nature of folk stories and belief systems in the ancient world, it is necessary to draw a great deal from more contemporary ethnographic data. Nearly all people tell stories for entertainment and nearly all people make distinctions that separate stories to be told (what we call legends) from stories that are regarded as fictional (what we call folktales, or in their water-down, literary form, fairytales). The distinctions here are not perfect because the folk didn't always behave themselves: some folktales drifted into legend and legends into folktales, but the rough distinctions are appropriate here to set up the discussion.

Whether the stories in question were legends or folktales, they needed to be entertaining AND they needed to draw upon (rather than contradict) the existing belief system. Just because a story was not to be believed did not mean that the storyteller could or would invent all sorts of fantastic elements to suit himself/herself. Those are the parameters within which pre-modern societies tended to operate, and it is a good assumption that the same was true of the ancient world and the stories they told.

"Mythology" is a tricky word because in involves the transmutation of oral tradition into written text (see my additional comment on the definition of these terms). But in general, what we regard as the mythology of the ancient world are the really good stories, some of which were told to be believed and some of which may have been told as fiction - but all of which were regarded as good entertainment. We cannot know for certain whether authors of the ancient world were inventing their own stories - building their own universe as you say in your comparison to the TV show (which I do not know) - but frankly, I doubt it. It seems more likely that those who wrote down stories were drawing from material they heard rather than what they invented. Either way, the stories could only operate within the existing belief system, so the stories necessarily draw on supernatural beings who existed and behaved within the parameters of the existing folk culture.

In short, how do we know these are religious stories about belief? We may not know the answer to this in those terms, but we do know they were good stories that incorporated elements from the existing belief systems. A story about a ghost in the Old Testament is a religious story about belief; a story about a ghost that is not in the Old Testament is a story that draws upon and likely reinforces belief. In essence, there is little difference between the two except context.