The Outer Space Treaty is a treaty between governments. As a rule, treaties only apply to governments. So SpaceX can say whatever they like in a document, as it

The Outer Space Treaty is a treaty between governments. As a rule, treaties only apply to governments. So SpaceX can say whatever they like in a document, as it's legal to do so in the US and then act upon it based on US law. From my understanding this means that they can claim it all they like, but if they tried to enforce that claim against anyone it wouldn't work.