You are correct.
But images usually get deleted off of a server.
The law right now is still pretty vague on internet stuff. That is why we copyright with the Copyright office all of our images on our web site.
It is cheap to do and it gives a level of protection that is pretty scary when you present a lawyer with an actual copyright certificate.
But it's not just images that are copyrighted. Anything written is copyrighted as well, as well as any created work. By law it is copyrighted the moment it is created, whether it is registered with the Copyright office or not. I really don't see how the owners of archive.org have a leg to stand on.