Maybe if the Angosian government had been honest about the situation and tried not to be utter assholes, Picard may have then been more inclined to help.
Problem is that Picard himself acts like a complete a-hole to the Angosian government. Would it not have been better, and perhaps more in tune with the message of the episode if Picard tried and convince the Prime Minister that he understands the situation they face by referring to Earth's history? He could have said that Earth itself faced similar circumstances when the War that their soldiers fought in was over. It would have been so much better if Picard actually tried to get the Prime Minister to come to an understanding, instead choosing to lecture and berate him in a way that doesn't resolve anything.