I thought at one point in time, it was agreed on that no single nation "owned" the moon. Therefore, what happens if someone goes up there for a commercial project and sells material gathered there? Is it "first come, first to profit"?
The Outer Space Treaty
Article II: "Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means."
Article I says, in part, "Outer space, including the moon and other celestial bodies, shall be free for exploration and use by all States without discrimination of any kind, on a basis of equality and in accordance with international law". I would look to maritime law regarding resources in international waters as a basis for how lunar resources might be handled.
Article VI says, in part, "States Parties to the Treaty shall bear international responsibility for national activities in outer space, including the moon and other celestial bodies, whether such activities are carried on by governmental agencies or by non-governmental entities, and for assuring that national activities are carried out in conformity with the provisions set forth in the present Treaty. The activities of non-governmental entities in outer space, including the moon and other celestial bodies, shall require authorization and continuing supervision by the appropriate State Party to the Treaty." Since this is a US company they will need authorization from and supervision by the federal government.