Iraq war and trumped up reasons
Although it would be a full time job to show a person skeptical of Conspiracies by their own government some proof, it does happen occasionally.
The Iraq invasion by America is of course for other reasons than stated, like most wars. Some Iraqis say that that is okay, because Hussein was terrible. Nevertheless the war should show that you really can't trust what government tells you.
For the people who think that the war secures oil to the West - supposedly no oil is leaving Iraq, it's going in to feed the US Army.