In many cases those store brand products are made by the same manufacturer as the brand names, but I don't think Amazon typically negotiates with the original product owner for manufacturing their clone.
Most of the Amazon X products I can think of are really basic obvious things. Sheets, cables, simple computer peripherals... well OK those are the things I remember ordering offhand that were such things.
My point is that they'd be categorized as basic staple items. Someone else might have sold a particular size or feature of X, but I don't see any reason why Amazon or another competitor wouldn't think to copy it.
Instead (as I made in a different reply a couple hours before yours) I believe it's the strength of Brand Recognition as a form of Quality Control, which is an area that has decayed on Amazon as a whole but less so with their own brand of products.
Not all of their products are "Amazon Basics" products - they have a lot of private label brands that aren't obviously "Amazon".
But the article I referenced above was a company that came out with a nice laptop stand design and a few months later, Amazon started selling one of their own that looked basically the same (but not identical).
