Something incontestable can't be argued with — it's absolutely true or right. It's an incontestable fact that the earth rotates around the sun.
You can't dispute something that's truly incontestable, because it's absolutely clear and unmistakably true. The witness to a car accident could say that it's the incontestable fault of the driver who ran a red light. And once you've signed all the necessary forms and been handed the keys, you're the incontestable owner of your new car. Incontestable adds the "not" prefix, in-, to contestable, "opposable," or "arguable."