The reason why transactions are denominated and settled in US dollars is because of the perceived stability of its value and the openness of the US financial system to international trade.

No, it's because the oil trade is conducted in dollars (the point of America's adventures in the middle east are ultimately to enforce this). This creates a demand for dollars, despite the US having the largest trade deficits in human history (which for any other country, would have made their currency worth less than the paper it was printed on).