Here is a good explanation of how they got from “freedom” to that. An important aspect of freedom is self ownership (if someone else owns you, you are not free), and:

If you use your body to pick fruit, that fruit becomes yours, even though you didn’t make it. If you use your body to land on Tristan de Cunha and plant a flag there and maybe pick some coconuts, that makes Tristan de Cunha and everything on your property and that of your heirs forever, even though you definitely didn’t make the island. And if someone else lands on Tristan de Cunha the day after you, you by right control every facet of their life on the island and they have to do whatever you say or else leave.