The basic Basilisk story is "Both of them should have known better". Godric Griffindor was boasting of how safe Hogwarts was (the way e.g. Hagrid does and Dumbledore believes in the book) and Salazar, being a bit of a troll told him to stop that. And that without altering any of the wards he could sneak a dragon or even a basilisk into Hogwarts. Now the last thing you should ever do with someone like Salazar Slytherin is tell him he's full of it and there's no way he can do [thing] - and Godric of course told him that it was impossible. So he did just that just after the kids had all gone home and told Godric what he'd done and that if Godric thought Hogwarts was so safe he could find the basilisk. And Godric blew his top of course.