"Who owns what" is a fundamental question of civilization, and how a culture chooses to answer this question is central to how the civilization develops.
And I saw a ton of knee-jerk reactions in every discussion about this. I see three very different concerns -- and I don't see anyone at all recognizing that all three concerns are valid.
If no entity can own property off-Earth - as is currently the terms of the space treaty we signed in, what, 1969 - there is a real danger that we, as a race, will never develop or make use of off-planet resources. And it is my firm conviction that we will desperately need to make use of off-planet resources.
If private entities are allowed to own property off-Earth, it is inevitable that claims to most property will be made quickly by the wealthiest among us, who will then extract rents in perpetuity. We've seen this many times before - corporatocracy and robber barons reduce everyone else essentially to serfs, or at best renters.
If only governments are allowed to own property off-Earth, I worry about the potentials for war, tyranny, and central control over humanity.
Any solution to using resources beyond our planet has to confront all three. And I'm certain that I don't trust anyone who doesn't at least acknowledge all three as real dangers.
There is of course the possibility that a representative government, beholden to the will of a free people informed by reliable experts and kept abreast of real events by aggressive free reporting, debating issues in public fora, might manage these resources in a way that avoids these dangers.
And while that seems unrealistic, it also seems (to me, so far as I have watched humanity) that - while this proposal is not wholly immune to any of the three dangers above - all other solutions I've seen so far have much more potential to fail in one of those three ways.