You don't need dollars to buy oil. Oil is currently sold in other currencies as well. In fact, it doesn't matter what currency it's sold in, as you can easily exchange currencies in the market.
"More than a third of our petroleum, about 37% of our total usage, is produced domestically by our own oil companies. I'm not sure why people seem to forget about those guys, ExxonMobil and Chevron and all of them; you may resent them but they are the principal source of our non-foreign-dependent energy. So this means that only a bit less than two thirds of our petroleum is imported. That still means most of our petroleum comes from OPEC, right? Wrong. Most of our petroleum imports come from non-OPEC countries; 56% of it, in fact. Of that 56%, the majority is from Canada and Mexico, who are about as far removed from the Middle East as can be. The rest of it is from other random places like Angola, Russia, the Virgin Islands, and Brazil [...]"
As long as you need dollars to buy oil, we'll continue with nonsensical debate like this.