Let's look at how the petrodollar came about. The first step with the run on gold in 1971 which broke the Breton Woods system. The value of the dollar went through the floor. Having a big navy didn't make any difference. This hurt oil exporters because now their dollar earning weren't worth as much, but they didn't abandon dollars. There was no credible alternative, and there was no military dimension to that fact.
Then in 1973 US support for Israel lead to the OPEC oil embargo. Oil prices quadrupled. You could say it was American military aid that caused this, well maybe but no actual projection of force by the US was involved. Military aid to Israel was no different in character from Soviet aid to Arab regimes. The reasons the embargo mattered and had an effect were economic reasons, not military ones.
When the United States-Saudi Arabian Joint Commission on Economic Cooperation was established in 1979 the US hadn't invaded any Middle Eastern nation, hadn't blockaded any Middle Eastern ports, hadn't established any bases in the Middle East. The total of their interference was support for Israel, a small state a long way from any of the actual oil.
All three of those milestones were entirely economic in character. Military power projection played no part in them. The US has and uses economic power anyway, regardless of how effective it's navy or army is. It was a military midget, but economic powerhouse in 1941 when Japan attacked Pearl Harbour. It parlayed that economic power into military might, not the other way around. By the end of the war the US was launching 2 aircraft carriers per month due to sheer economic muscle.
US military intervention in the Middle East long post-dates the establishment of the petro-dollar. Those claiming the petro-dollar is a result of military power have it exactly the wrong way around.
