A bit of a bump here but I've just experienced the same thing - I bought something on eBay and it arrived from Amazon Prime. Strangely enough, even after searching on Amazon for exactly the same item description, I still can't find it. I also searched there before I bought from eBay.
I'm happy with the price I paid (it was still the cheapest I could find) but I thought that I'd ask Amazon support if this dropshipping using Prime is actually legit.
It turns out that it is allowed, providing it's shipped from Amazon as a 'gift'. No T&Cs are being broken at all according to their chat representative "Douglas".