Sorry, are they claiming that they own the rights to lists of publications, not just the publications themselves? Like, I’m not even allowed to have the titles of books without their permission?

Fighting against sites like Anna’s & The Internet Archive is pretty much on par with advocating book burning in my opinion. I understand why some might disagree, but for me there’s really nothing to debate. Some people want to remove access to education from people who might not otherwise have it, stupefying society in the process, to make probably not a whole lot more money and to possibly live a little more affluently than they already do.