IIRC, many traditional white label brands are actually manufactured by the name brands themselves, and they're part of a strategy to segment the market.
The difference here seems to be that Amazon has been cloning relatively unique products made by smaller companies, while traditional white label brands are fungible commodities made by large players with little differentiation. From the OP:
> Because of the limitations of shelf space, traditional retailers stock far fewer products than Amazon’s hundreds millions of items. Typically, they create private-label products to compete in generic categories such as paper towels, rather than copycat versions of items created by smaller entrepreneurs, private-label executives said.