Out of curiosity, what happens if a second company (say, Anglo Platinum) goes out there and blows up the facilities of these guys? Maybe even murders their miners (if there are to be any humans out there). What would the legal protection be?
"Out of curiosity, what happens if a second company (say, Anglo Platinum) goes out there and blows up the facilities of these guys?"
War.
However, the good news is that even on Earth the benefits of cooperation tend to outweigh the benefits of aggression, in space for the foreseeable future it will be even more so. It is so, so easy to trash a space facility and so, so hard to defend against it that in essence all private companies in space will de facto be in a MAD situation should they decide to go that route. It will be a long time before anyone will have a position where they can afford to attack somebody and have a reasonable expectation of survival.