why wouldn't they trust Picard? They had no reason not to trust him, he'd done nothing but try to help them. And again, the plot never has Dougherty or Picard explicitly explain what the Son'a technology could do for billions across the galaxy. Now why do you think that is? Because they didn't want a scene where the Baku say no to leaving their planet and resettling to help billions. It just wouldn't have worked.
Because he was a representative of the same people who came to move them? So what if he outwardly appeared genial and conciliatory? Should they be naive enough to take that at face value, after what they'd been through?
You are still harping on the Ba'ku being forced to leave, when that is absolutely not the only choice possible here.
The rings, we are told, regenerate constantly, or at least they will, until the collector sucks all the magic out of them for good, which will make the planet uninhabitable "for generations." So, the Federation would take what is apparently a renewable resource and turn it into a non-renewable one, in order to make it more convenient.
That is worth questioning, too.
There's no indication given in the film that the Ba'ku would be against other settlements on the planet, as long as they respected the Ba'ku way, or at least didn't shit up the place too much.
Locutus went into this in some detail so I'm not going to repeat him. Suffice it to say, making it a binary choice between "Ba'ku stay" and "Ba'ku go" ignores the other possibilities, and it's the only way to make your argument work.
They choose
keeping their homes over helping billions of people
they do not know and have no interest in.
Tell me, how much do
you go without so you can help people you've never met? Would you give up your home for the benefit of strangers if asked? Would you be okay with being deceived into it? What about being forced to at gunpoint?
Those are the scenarios you are promoting.
The group in question is not the issue. I wouldn't care if it's the Ba'ku, a tribe of Native Americans, or a colony of sentient garden gnomes. Forcing people to leave their homes to benefit others is wrong.
Actually the Ba'ku didn't know who the Son'a were until after Picard told them they were both from the same race
Seems kind of weird that they wouldn't recognize their own kin, but it's been a while since I saw the movie, so you may be right.