No. __Their__ petrodollars. It's their oil. The demand for their oil doesn't just come from America. In fact, America isn't even the largest individual buyer of Saudi crude and constitutes a small percentage of total destination of their crude.
Still doesn't make it "America's" money (which the previous poster was implying). If anything, pricing the worlds energy in dollars (and thereby ensuring that the global demand for $'s remains high) allows the US Fed to get away with "printing money" as much as they do, without totally debasing their currency.
It's interesting to note how Iraq's threat to start pricing oil in other currencies (was it the Euro they mentioned?) is widely regarded as one of the precursors to America's invasion and occupation.
So those "political reasons" you're alluding to work both ways.