What does the poet mean by “Or so the story’s told”?

“Or so the story’s told” means the poet is unsure about the authenticity or accuracy of the incident he is narrating. It is a story which floats on the oral level and he has only heard it. Though the above quoted line follows the line “Each one possessed a stick of wood”, I think, it essentially is not concerned with that mere information of each person possessing a log. Rather on a general level, it indicates to the lack of authenticity of the story.