That's not how copyright works.Well, the same thing goes for archive.org. But if it's not public content, why put it on a public web server?
Compare it to the physical world: Pieces of artwork are on display in publicly accessible spaces which are being rented, but it's obvious to everybody that it's someone's intellectual property and that someone is also a copyright holder. If the copyright is infringed, the law will be on the copyright holder's side. The digital world is a subset of the physical world, where laws also apply.