Given that there are so many unused systems, how does one acquire the right to colonize one with a title that others will recognize?

Example: Red colonists start a new agricultural colony at Paradise. The planet has berylium spheres that strip mining will access, but so doing will toxify the atmosphere. The Mantis people arrive with their mining equipment.

Do the Reds have a case the Mantis folk will honor? Is there any legal recourse? Do the Reds have to fight or flee?

Or is this where the PCs step in and agree to help the Reds until the Mantis offer more?