It will be wholly dependent on global oil prices even if refining stage had nothing to do with it. Just because oil producers have a choice of selling their oil

It will be wholly dependent on global oil prices even if refining stage had nothing to do with it. Just because oil producers have a choice of selling their oil at home or abroad, and refinery owners have choice of buying their inputs from local or overseas producers, and petrol station chains have a (rather limited and almost not used in practice) choice of buying the gas they sell, from local or overseas refiners too. Markets are global. You can only "disconnect" the prices by banning foreign trade in oil and oil products. But that wouldn't work out because you need both heavy and light crude to produce most refined product, and there's almost no heavy crude produced in US, and you need to sell excess light crude (which is by the way more expensive and rare in the world overall), somewhere. Also, if your goal is reducing gas prices, disconnecting markets by banning foreign trade isn't an answer anyway, even if we ignore light/heavy crude problem. With significantly reduced prices, oil production will fall and eventually, imports will be needed again to provide necessary amounts for the market. America already has by far cheapest gas of the developed countries. Reducing it even further won't make anyone much benefit.