This happened to me on eBay with a handmade item listed for sale (someone did a crackerjack job of PHOTOSHOPPING half of MY work on their shoddy P.O.S. handmade), and while they weren't as nasty as Etsy is being to you, it was a HUGE headache to get the images pulled. I do understand the need to "prove" that they are indeed your images, but beyond that, these companies don't get that it's actually rather traumatic to have your property (even if it's just a photo) stolen and passed off as someone else's.
I routinely see my graphics reposted, redistributed, and sometimes stolen online. I've been getting a lot of strange hotlink hits on certain (mostly Jane Austen) images uploaded to my Photobucket, and believe it or not, there are 2 or 3 Facebook "Flair" buttons that have been made using my images...I haven't even bothered to try and report those or get them taken down.