From what I understand most of those "house brand" products are made by the same factories of the on-brand stuff, probably but not necessarily with the same recipe and QC standards.

Product branding has almost no relationship to which company actually made the product, consumers are intentionally blinded to this information. I would appreciate regulation requiring products to be branded with the factory that made it; I think this would be a huge win for both consumers and workers but it would be firmly counter to the interests of major brands with a lot of political influence. Also many consumers would probably oppose this against their own rational interests because they have personal attachments to brands.