Oil companies swap base gasoline all the time.....
Let's say I have a refinery in Houston and you have one in Dallas. It makes little sense for me to truck my Houston gasoline to Dallas and for you to truck your gasoline from Dallas to Houston when gasoline is a commodity product. So, I let you draw 100,000 gallons of base gasoline from my storage tank in Houston for your Houston gas stations, and you let me draw 100,000 gallons of base gasoline from your Dallas holding tanks for my Dallas gas stations. That way, we both save on shipping.
Texaco gasoline may have come from a Shell refinery and vice-versa. At a gasoline terminal you may see trucks from up to six different companies all loading at the SAME terminal (that for example may be supplied exclusively by Shell). What comes next, however, is what makes Texaco Texaco and Shell Shell. Additive.
Each company has its own additive and adds it to the base gasoline. So while the base gasoline may be the same, the additive is different, and hence the brand of gasoline you use is different because of the additive, not the base gasoline.