Until 1973 the US dollar was on a gold standard, but Richard Nixon took the US off the standard in 1973. Actually abandoned the system in order to print inflated currency called Greenbacks without any commodity backing.
Part of the Nixon shock at the same time was the attempt to reach out to China to establish trade and that has been a massive part of the story. China was literally starving itself to death despite being the size of an empire they were tied up in stupid communist practise. Its probably more arguable that Dollar has become greatly supported by cheaper China production and labour then the oil aspect alone.
The big deal now going forward is that China has a falling working population, this equates to a rapidly rising cost of labour. Thats ok, they start from a low base and can develop the economy however it does make it likely that competetion between USA and China occurs as they both must be the most efficient to justify trade.
The deal with Oil recently would be USA has greatly upped its production, however any figures you take must deduct USA consumption also and that is too great to call USA oil backed. Its a global reserve currency