It's difficult to ascertain who manufactures private label oil.
You may find something digging around the api site at: http://eolcs.api.org/DisplayBrandNames.asp
The maker of shop-rite oil (a supermarket in NJ, NY CT ) surfaced on this page. Honda oil looks interesting on this page also as it is listed under American Honda, and Apollo America Corporation. I wonder if this company called apollo http://www.apolloamerica.com/apollostry.htm makes Honda oil.
I had a private e-mail from some mystery lurker who assured me this was real true genu-wine Quaker State. Apparently some of the shipping containers are labeled as such. This is in line with what the K-Mart manager told me, but not in line with what Johnny the PZ/QS (and now Shell) expert said.
I should add that we've spent a lot more time on Wal-Mart's house brand, and it's still up in the air as to what exactly that is. It was made by the QS subsidiary in Shreveport and speculation is that some production will be shunted to Shell to make up for the departure of Texaco (Equilon), on the other hand there is also evidence that some of it is Warren out of Omaha the manufacturer (and it IS labeled) of Sears Spectrum oil.
If it comes from Shreveport it's almost certainly the same thing as Wal-Mart's house brand. It won't be coming from there for long since that plant is due to be closed. Shell would be my best bet for the new formulation.
I should add that if I remember correctly Shell varied all over the place depending on location. I think that information was in the Consumer Reports oil test from several years ago.
I should probably qualify by saying that the old Equilon plants probably have the most capacity since the Havoline name went to Chevron.