You should know WM is continually looking for lower priced suppliers. Like any of these companies they give a contract to supply x amount of products. The next time they need to fill the warehouse with this item, a new lower bidder may get the contract. To WM its all about getting the cheapest, nothing else is of concern because motor oil is just a commodity to them, all is the same, the brand or who makes/supplies it means nothing to WM.
Btw-Even though a major oil company may be the supplier is no reason to assume its the very same formulation.
I fella I have known all my life is a route distr. for a large well known bakery chain serving nearly 50 stores and restaurants on his route They (the bakery owned by nat't chain) also make WM brand bread (in this region, about 1/2 doz stores he claims) as well as several local grocery store chain. According to him the bread in the WM and other store brands is the same bread but its not the same exact bread as his national brand. He places the stores brand on these shelves, he said they are all the same but not the same as the name on his truck.
So just like there are many difference recipes and qualities of ingredients to make bread, there are many recipes and qualities of ingredients to make motor oil.
So assuming because one major company makes its the same product is a false assumption. If the bakeries have a different bread you can bet the oil companies have a different oil for the WM brand. I know the bread is different because I have eaten it. While the local brands are fine, the national brand does taste better IMO.