And that's basically the point for everything Amazon does. They aren't doing anything other companies don't, it's just they do it on a massive scale.
With "store brand" specifically, the idea is that Equate or other store brands were well known to be comparable, if slightly less good versions of name brands. In economics terms they were "substitute goods" from brand names, but depending on quality they may not be "perfect substitutes."
In the case of Amazon, if they have brands that are at first glance not Amazon brands, but actually are amazon brands, then they are kind of doing an end run around what was an implicit agreement between consumers and retailers. Namely that a retailer will make it explicitly clear, with obvious branding, what is a "store brand" and what is not. Simply stating "our brands" isn't obvious enough to make that connection if you are only spending 30 seconds on a product description page.
This is something that Amazon is great at actually.