Oil prices in this case is a broad term. Countries that can refine crude prefer to do so, as it makes a lot of money. At the end of the day, the normal person at the gast station doesn't care if the crude was cheaper or more expensive. They care about what they pay for gasoline.

More specific to the infrastructure often the oil is directly delivered to the refinery and only the refined products make it onto the market at all. So by cutting off the refinery also the oil exploration that comes before is cut off from the market.

Prices are determined based on supply and demand, so any event which decreases the global supply, even in sectors where most of the world was not being given market access, will drive the price up for everyone else.

This is why Biden has been approving drilling projects left and right while transitioning America off the stuff, America's prices are subsidized, but the world gets squeezed big time by supply fluctuations elsewhere, it's basically a spooky action at a distance way to try and subsidize global prices to artificially keep them low same as America's oil prices.