That merely outlines the problem with Zazzle. They not only respond to DMCA notices by taking down the offended materials (just like an ISP), but they also preemptively police the environment by themselves and take down anything they suspect is copyright infringement.
I once made a t-shirt with an old Albert Einstein picture and they immediately took it down, asking me if I had the permission to reproduce this image. I had to send them a link to The Library of Congress page where I downloaded the image, pointing out that this picture belongs to the public domain. They can ignore a lot of stuff but they won't.
That's interesting; because I think I recall something in the language of the safe harbor law where if a content hoster starts actively policing their own content, they can be held liable for anything that slips through their net.
They have no case.