How can truth be different than fact, especially when it comes to storytelling (and novel writing)? What purpose do Billy's stories serve in the narrative?

Billy tells several stories on the canal over the course of the novel, which are often a mix of fact and fiction. He describes his stories as capturing "a version of the truth…A storyteller's version." How can truth be different than fact, especially when it comes to storytelling (and novel writing)? What purpose do Billy's stories serve in the narrative?

A fact is a simple statement: It is bitterly cold outside. (Can you tell it is February in Iowa?) The truth is: While the weather appears bright and beautiful, people are freezing the death, dogs are left to suffer (and die), and cabin fever can set in. Billy's stories probably aren't at all factual, but they do hold truths, sometimes small, sometimes large, that help each woman come to some realization about herself.

Facts are statements of something concrete and provable. Truth is an accurate statement of facts. Fiction and storytelling are exaggerations of facts with enhancements meant to teach a lesson or convince the listener or reader of a point of view --the exaggerations and enhancements add bias to the facts which then can render something based on fact that is no longer true. I think Billie's stories are the lesson teaching kind--parables, if you'd like or an Aesop fable.

Stories are told to illuminate a truth. News is a recitation of facts with the possible addition of opinion. Billy tells stories to share the truth of life on the canals. How communities emerge only to separate into individual lives.

I recently read The Things They Carried, by Tim O'Brien. The short stories were written about the Vietnam War, and the author did serve. A lot of my reading time was spent trying to figure out which parts of the stories were true and which weren't. One of the points he made was that there is "story truth" and "happening truth," and how sometimes fiction can project the core truth of an event better than the actual facts. I think that's true of Billy's stories, too, that they're meant to illustrate life on the canal better than a recitation of facts could.

Sometimes facts alone are insufficient to convey the greater truth. The greater truth involves relationships, emotions, climate, setting, cultural practices, context, and more.
Billy’s stories may be bullshit when it comes to the facts, but they are incredibly effective when it comes to conveying the greater truth.