No. First-party retailers don't generally commingle stock with other third-party retailers. They typically have few suppliers, often one supplier, for each good. That's for many reasons, but it also makes it easy for them to identify who sent them counterfeits.
Amazon is discovering what old-fashioned retailers learned long ago: customers do not give a fuck who, ultimately, has injected the counterfeit. They will blame the retailer.
If I was Wal-Mart I would be absolutely hammering this point to customers. I'd be running ads about "Shamazon". Tearful mothers whose child got sick. Teens who saved up for a game system or phone and got a block of wood. Grandparents who bought medical equipment and got a faulty knockoff. Everything dangerous, disgusting, outrageous or even just annoying. I'd be carpet-bombing every channel with ads amplifying the message that Amazon can't guarantee what you get. Wal-Mart aren't saints, but their historical success has rested heavily on an incredibly tight grip of their supply chain and logistics. They do actually know what they have on the shelf.