The gas at most stations all comes from the same distribution center. BP may supply one area and Gulf another and a third is an independent distributor who buys it from the other two. There may be different additives added at the different brand stations, or not.
I have heard time and time again, about how bad gas caused this or that problem. Not really likely. The wrong gas (wrong octane for your car) can be a problem, but bad gas is not the problem most people think.
In over 40 years of driving, I have had fuel twice. Both cases was a result of water due to a problem at the specific station. (one diesel the other gasoline.
Real problems due to bad fuel is really rare.