Stories can be useful. You could say [arbitrary example] that "I'm trustworthy", or you could tell a story of the time you were given privileged information and didn't use it for personal gain.
The story is much more convincing, because it invokes empathy from the audience. The trick is to tell a good story. That means understanding plot, characters, tempo, your audience, and so on.
Not saying it's the be-all and end-all, but when done right stories have their place.
