I don't think Picard was in any danger of losing his ship, I think the Starfleet Admirals who reviewed the case would have the same reaction we do: "Anyone who thinks the prime directive means you can't save innocent people from certain death because of moral Butterfly Effect anxiety is a moron, case dismissed."
Good interpretation of the prime directive:
Vedek Winn is anti-Federation. Vedek Bareil is pro-Federation. Prime directive says, we do not intervene and try to install Vedek Bareil even though it would be in our political best interest. (In other words, screw you Henry Kissinger you sociopathic war criminal).
Moronic interpretation of the prime directive:
We could save this planet by pressing a button, we choose not to because maybe somebody on it will be the next Hitler.