Some people want to live in isolation. It's their choice.
They settled the world as colony before the Federation existed. Even in our own history people have settled in new places for a vareity of reasons.
So the reason why the settled the world is not important, the fact that they did is important.
It doesn't change the fact that they are subject to shifting political winds of the galaxy around them. Tomorrow the Federation could sign a new treaty with the "name an empire" and ownership of the Briar Patch would shift. And the new owner would be under no obligation to placate six hundred colonists (which is what they are since many of the first generation Ba'ku are still around) sitting on a fountain of youth.
It's along the lines of the old mantra "those who don't vote don't get to bitch about whose in charge". The Ba'ku didn't care about the galaxy around them and ended up not being in control of their own destiny.