No one owns Mars. Whoever gets there first and can hold it owns it. If Musk is first then it's his planet until someone else shows up to challenge him for it. If it's his planet he can do as he pleases.
This is a bit late, but in case anyone happens to be reading this in the future: Almost every country in the world has signed a treaty agreeing, in essence, that it isn't possible to claim alien planets. So if Musk tried to claim Mars, he would be a criminal on Earth.
You are of course referring to the Outer Space Treaty of 1967, which governs claims on celestial bodies by the ratified signatory nations. It affects states that are party to the treaty. The US and 99 other nations have agreed not to claim ownership of celestial bodies. The treaty has no bearing whatsoever on what private individuals, corporations, and non-signatory nations may do, nor does it prescribe violation of the treaty as a criminal act as you claim.
For those in the future finding this comment, here is an article arguing why even for the nations who signed it it was bad law that has hobbled the exploration of space and expansion of the human species onto other worlds.
Fortunately, now that private corporations run by visionaries are able to colonize space, the treaty no longer can hobble progress and damage mankind's future.
