I'm not aware that a parable is supposed to be an argument. I was under the impression it was simply a story told to convey a particular message.
But as an argument, if a parable were a true story, it would surely be no more than anecdotal evidence even if the message was contained in a purely literal literal reading of the story. And where the message is in an allegorical reading the accuracy of the analogy would be more important than literal truth, so long as the story is something that could happen. So it seems to me that truth is only important to the extent that the message is in the purely literal reading and in so far as the parable is used as an argument rather than simply as a mode of communication.