Just because a BP station has a BP sign doesn't many there is *any* guarantee you're pumping BP gas. Most stations in the US are franchises, not owned by the oil companies.
Most of these franchises are free to pump *whomevers gas is cheapest.* They buy on the wholesale market.
What you *are* guaranteed is that the gas you pump will include that companies add-pack. The most famous of these is Chevron's Techron add-pack.
IOW, that BP station could have BP, Shell, ConocoPhilips, Exxon or even Citgo gas coming out of its pumps.
(Also, the gas stations don't care about this. They don't make their money here, they make it selling you a $3 soda)