Well a company's "claim" on any extraterrestrial land would only be "valid" or enforceable if it is recongnized by a government body, right?
Maybe.
But if the company simply starts using their privately-owned vehicles to ship hordes of employees to basically colonize, say, an asteroid, they don't really require the recognition of an Earth government.
It would be different if they used NASA shuttles to get the project started. That would obviously require the consent of the American government.
But as space tech companies grown, and become able to mass-produce their vehicles and equipment
without government money, I foresee the need for government recognition falling to the wayside.
"We found it, we colonized it, therefore it's ours no matter what you guys back on Earth say."
Kinda the same mentality taken by some of the early American colonists regarding the treaties between England and the Native tribes.