eBay already prohibits listing an item on eBay then purchasing the item with your Amazon Prime Account so you get free 2-day shipping. When you do this, the eBay buyer gets a gift receipt from Amazon in the box, and when that happens they often get upset and complain to eBay as well as leaving you a negative feedback.
Many sellers (including me until recently) list items on eBay and use the Amazon fulfillment service to ship the product to the eBay buyer.
This still allowed by eBay as long as you are shipping your own inventory. However, eBay Australia has recently banned the practice leaving many sellers to think it’s just a matter of time until eBay U.S. does this here as well.