Now, the buyer and seller can of course convert USD from/to their desired currency on FX markets. Oil trades tend to be big, so that would cause demand for USD liquidity. That demand, and the fact that these dollars are effectively "locked" inside the FX markets (reducing supply), would make the dollar price go up (everything else being equal), hence strengthening the dollar.
[1] https://en.wikipedia.org/wiki/List_of_countries_by_oil_produ...
Which is the point I'm making - expand your view beyond just buying and selling the oil, and think how you get into the position in the first place. From the ground to where it is used.
Whatever currency you hold those selling oil will take for their oil - because there is a big financial system whose job it is to make that happen and to shuffle the currency holdings around until everybody holds what they want to hold.
The FX system is part of the oil market. It lubricates the parts oil can't reach.
This is called settlement overhead, and is the reason you're incorrect. Every time you change one currency for another on any meaningful scale, it eats into your profit margin..
Tl;Dr - there's no such thing as "no foreign transaction fee!!!1!" in oil baron sized transactions.
This is sometimes referred to as the network effect.
Fundamentally in every real transaction in the world the seller gets the currency they want to hold and the buyer gets to use the currency they earn in. Because otherwise there is no deal.
The whole purpose of the global financial system is to sort out those mismatches so deals get done - and make a turn while doing so.