Lawmage: Not exactly, Dax. Were we in Germany and Japan with the permission of their governments five years after the start of World War II? When did we transition to something other than an Army of Occupation?
We conquered the countries you mentioned, so there was no need for governmental permission to "occupy" them. A vanquished government hasn't got much say about who will be staying in their country.
Both "axis powers" transitioned into peaceful co-existence with the US, and, as always happens when we conquer a country, became our allies and trading partners.
In S. Korea, we fought on their side against the Norks, got them to a stalemate, and stayed. It would be foolish to think that the S. Koreans didn't want us there at the time as protection against the north.
Iraq presents a different problem, since they didn't attack us, declare war on us, or threaten us. We basically put ourselves there. We aren't there because we vanquished an enemy, since Iraq was not our enemy in any effective way.
And as the entire Iraq invasion and subsequent battles were based on very little except false information, faulty information, cooked up information, and outright lies, in fact was based on nothing more than the President's desire to invade Iraq, the comparison with Germany, Japan and S. Korea fails.