That may or may not be true, having been in the oil/gas industry myself, even working directly on some of the drilling platforms, there is a lot of collaboration between major oil producers, and in many instances, several companies own oil rights in certain areas of the Gulf of Mexico for example, it is not impossible but rather highly likely that you will see more than one major producer owning partial shares on ONE lease (which may contain several platforms/wells), and even operating off of some of the same platforms. Reason being, there are only so many leases available, land or sea. Same is true for pipelines, there are only so many miles of pipeline available to ship crude oil in and refined product out. Basically, average folks, those that don't work directly in the industry, don't see the combined effort, just the competition between the brands.
By the same token, there are only so many companies that have the capability of refining crude oil into the usable products we pump into our cars and trucks. Despite the fact that it is technically an Exxon/Mobil refinery, there are other oil companies that own a stake in that refinery as well. These are typically your smaller, no-name companies no one has ever heard of that do not have the capacity to drill or refine the crude on their own.
After the refining process, finished product is then shipped off via pipeline, barge, rail/tanker car most often to storage terminals, there again operated by more than one company for later sale at their retail locations.
Basically, I agree with MikeD simply because the crude coming into the refinery is the same no matter which company operates the platform, the refining process is the same, so the end product is the same. At exactly which point in the process the different additives used by different companies for different markets/regulations etc., are added is a good question that I would like to look into further myself, but essentially, there are limited production/refining/storage and distribution systems in place for refined petroleum products which pretty much necessitates some collaboration on the part of oil companies, so the gas you buy from the Shell station could very well have originated from a BP platform, processed at an Exxon/Mobil refinery and so on.....
For the record, I have only run 87 octane Exxon/Mobil products in my vehicles. It was only when I ran the same grade but went to a variety of off-brand stores that I experienced problems, just my experience.