So they buy oil - what do the people that sold it to them do with those dollars?
Yes, those dollars can slosh around for a while, but eventually they either come back here or they get stored somewhere as reserve currency.
Either way is a win for us. If they come back to the US, well it helps the economy here. If they decide to store them under a mattress, we will have gotten goods in exchange for some pieces papers whose future value is not guaranteed.
All that money is going to go into the real estate market and balloon up prices so high that the average American will be a lifetime renter.