Based upon all of the above, I'm not sure what you're looking for, but I'll play.
I live in Ohio, and have never bought oil out of state, although I'd haul some home if the right deal presented itself.
In the past two years, I've bought motor oil from Walmart, Meijer, PepBoys, AAP, AZ, Big Lots, Kroger, O'Reilly and one private party on Craigslist in Columbus.
I usually buy on either a strong (cheap after) MIR deal or clearance.
WRT Walmart, SOPUS and XOM are pretty big players, and Chevron and Ashland are also decent sized.
I don't believe that any of these suppliers would cheapen their brands by offering a dumbed down product for Walmart.
Also, Walmart does offer top quality products in those name brands it chooses to stock.
It would benefit neither Walmart nor the name brand suppliers to offer a cheap Walmart-only product.
These vendors would suffer a hit to their carefully nurtured brands, and Walmart would suffer by gaining the reputation of selling only downgraded versions of name brand products.
Walmart does have its private label items, as well as some cheap Asian made stuff for those who look only at price.
Maybe I am naive, but I would bet my engines that the branded oils sold at Walmart are identical to those sold anywhere else.
I'm not one to accept the idea that everything is a vast consiracy, though, so I could be mistaken.