I do, and, apparently, coming from Amazon, "minimal and plastic-free" means that, if I order a single item, it will come in retail packaging (plastic tray to immobilize and cushion, inside a cardboard box that is at least 6 times the size of the product - hence the need for that plastic tray - inside shrinkwrap), and then that item will be placed inside another cardboard box that is at least 6 times the volume of the retail packaging for the item I ordered, so, in order to cushion it, I need a huge pile of those plastic air pillows.
It's a pretty huge amount of packaging and cushioning, about the amount you'd need if your package will be handled by drug-crazed chimpanzees (or USPS). But then it just gets loaded into the back seat of the car of whatever gig economy person does the Amazon deliveries in my neighborhood that day. I don't know what Amazon thinks these people are doing to necessitate that volume of packaging, or why they're continuing to employ them given that they think that is the case.
tl;dr, if they really were pushing for minimal packaging, I'd have expected a paper (or _maybe_ Tyvek, to protect against the elements) envelope with my address printed on it around the already-sufficient retail packaging, and nothing more.