Yes, this is what I though too. He just bought property rights. It's still part of whatever country it's located within and they can apply all of their legal code on you. I imaging digging deeper than a few feet would be illegal on that without proper authorization first. Having a really sovereign country is kind of difficult.

It is your property, but it's not your sovereign country. You still need to obey the law of the country your property is part of, and that severely restricts what you can do with it.