The veracity of any story is unimportant with one major exception. Where the story claims to be true it is very important. In fiction the story is expected not to be true but it must always be believable within the parameters of the fictional universe that the author creates. In allegory jokes and morality tails, if the story communicates the meaning that it is intended to then it’s truthfulness does not factor in to the equation. However all forms of stories that claim to be truthful, whether they fulfill that requirement or not is of the upmost importance, because writing should never misrepresent it’s self, and that matters in all writing.