Even when those platform sellers aren't selling through Amazon, all too often they're so trapped that the order still comes in an Amazon van and even from an Amazon warehouse. I'm no longer confused when my eBay order turns up in new Amazon packaging, but I certainly was at first - and I've just ordered from a shop's own website and it says it will come from Amazon.
But that did bring an example of how they're simultaneously stupid - todays order was shoes. Strangely enough I want them in my size. Amazon insists on trying to sell me "popular" options, i.e. the tiny sizes their captive sellers have overstocked