I don't know where you came up with this ridiculous claim, but not only is it absurd, but even if true their core business is not delivery. If you were right then Uber Eats couldn't exist.
The fact that it is being massively abused doesn't change the correctness of the original statement. One of the pillars used when determining whether someone is misclassified as a contractor is whether they are doing an essential core function of your business on an ongoing basis.
The only reason Uber or Uber Eats has managed to get away with their gross misclassification for as long as they have is because the federal law appears to never get enforced, practically speaking, except when someone sues, and they managed to trick the people of California into voting for Prop 22, which explicitly reclassifies rideshare and delivery drivers as contractors at the state level, reversing laws passed by the California legislature the year before.
But the GP is absolutely correct that delivery is a core part of Amazon's business. Without some form of delivery, Amazon would literally not exist. That strongly weighs towards employee status. As long as they were contracting with companies like UPS and FedEx that had their own branding, the lack of control and the ability to deliver other packages outweighed that factor, but I'm pretty sure all of the Amazon deliveries are done by vehicles with Amazon Prime branding on the vehicles, which tips that balance towards employee status.
IMO, there is a high risk of these drivers being found by the courts to be misclassified.