Dougherty wasn't "obviously wrong." And the Federation council only ordered a review.
The Federation didn't know that the Son'a and the Baku were related. Dougherty dragged the Federation into the internal affairs of another society. Something the Federation looks down on.
Basically, the Federation would've gotten the Baku off their planet for the Son'a and now they're aiding someone who has ketrecel white, which an enemy depends on. Maybe the Federation Council thought they could cut off a supply of ketrecel white to the Dominion but if the Son'a were already supplying the Dominion with ketrecel white, they wouldn't just sit back while the Son'a switch who they're partners with. They'd want to fight to keep the Son'a on their side, turning the Briar Patch into another warfront. The debate over whatever the Federation Council reviewed is the real conflict in
Insurrection. They should've brought that out more.
Then you're having a debate about the Dominion War but now it's actually being done on TNG terms where Picard has to fight to make his case. Or, to make it not so focused on the Dominion or DS9, it can just be a general "enemies of the Federation" argument.
Replace ketrecel white with something else that would give the Federation a tactical advantage and expand the focus to more than just the Dominion. They can reference the Borg, the Romulans, who the TNG Fans are familiar with, and then name-drop the Dominion as an easter egg for the Niners in the audience. And then the question becomes: Should the Federation break the Prime Directive to triumph against their enemies or will they have lost what really matters in the process? "Are there other ways?", Picard can ponder, and now this story feels relevant to Star Trek at large because the immediate situation they're dealing is just a microcosm for something larger in-universe. And it lets Picard test his moral metal.
In DS9 or DSC, the story would favor "the ends justify the means". But
Insurrection is TNG, so it's going to favor the opposite side of the argument. So Picard being Picard alone means you would've gotten a story that wouldn't have been told on DS9 with him dealing with an issue he didn't have to deal with in the TV series.