I don't understand how this story is a good anecdote for what this guy is trying to say ie, that some people have a sixth sense about hiring

How is it sixth sense that he fired a guy who obviously made such a grave mistake ?!

If the guy was fired before the mistake and he went to a new company where he committed a big mistake, then that would have better suited what he was trying to convey !

Obviously he shouldn't make up stories, but the one he uses doesn't suit the message