"The dollars printed to go overseas to buy oil and other stuff don't come back to cause inflation."
I think this part is wrong. When overseas oil companies get the dollars they are going to spend them, otherwise they wouldn't sell in the first place. If the economy worked the way you suggest I think we would see inflation from those dollars sent overseas for oil etc.
This article introduces a new term 'structural' for describing the US trade deficit.
Essentially if a country is to have their currency as the world's reserve currency then they have to run at a deficit.
Since all those extra dollars that get printed go overseas they are not in the US economy to cause price inflation, i.e. too much money chasing too few goods.