As a Costco shopper, I am also quite likely to grab the Kirkland brand instead of the competitor.
Most supermarkets, on the other hand, work with manufacturers that aren't name brands, and almost exclusively sell their store brand alongside name brand products.
While I don't know what makes Amazon's practices different from what supermarkets do, my assumption is that placing two products adjacent on a shelf is very different then highlighting and promoting the store brand above and ahead of the competition. The store brand doesn't appear exclusively in recommendations or ads or come with a "Preferred" badge. The store also doesn't use sales data to decide which products to make a store brand for, with the goal of overtaking the name brand.
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.