Oil is what really backs the USD. (See: "Reserve Currency").
The biggest army in the world is what backs the USD.
If it was oil, then it seems to me the country with the largest oil reserves would be the world's reserve currency.It might be the biggest army, but I think the dollar is the world's reserve currency because the US has the largest productive economy in the world backing it.
Unfortunately, we might be subject to a natural experiment in the next couple of decades that will show us the right answer; I can imagine that in 20 years the US still has the world's biggest army but some other nation has the world's largest economy.
It would be really cool if Bitcoin Nation were the world's largest economy by then...