Why all the concern over who makes the base stocks for Wal-Mart? Wally sets a specification and companies bid on the volume. Maker A, B, or C may be the successful bidder - who cares, if will be made to the Wal-Mart spec. Bids go out for the additive package speced by Wal-Mart, and finally a packager is selected.
The whole product, base oil, additive package, and packaging are speced by Wal-Mart. And what Wal-Mart wants Wal-Mart gets.
So if Wal-Mart specs a decent oil that is what we will get no matter who the components come from.
From my experience (non scientific) Wal-Mart generally does a pretty good job with house brands - kind of middle of the road - reasonable value for the price paid.