The supermarket fuel think is I think an urban myth.
I live close to the Kingsbury Fuel Terminal
https://www.eetfuels.com/our-locations/kingsbury-terminal/
Until about three years ago you could see tankers with every conceivable branding (supermarkets, Jet, Murco, etc, and premium brands) queueing up to fill from the same tanks. A neighbour who is an ADR qualified tanker driver confirmed the only difference was that the "pots" (tanker compartments) that were going to have premium high octane fuels, were dosed with an additive prior to filling with the same standard fuel.
Then suddenly most of the tankers became Hoyer branded tankers, apparently according to my neighbour, because too many drivers were becoming aware that there was little or no difference between brands, only between premium and standard fuel.