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.

Yeah, Anna's Archive bragged about doing it (and they did great).

A few months ago, the search engine expanded its offering by making available data from OCLC’s proprietary WorldCat database. Anna’s Archive scraped several terabytes of data over the course of a year and published roughly 700 million unique records online, for free.

Scraping data is now "hacking". Every single computer science department will have to close its doors and surrender their research datasets to the police.