"Statement from Brewster Kahle, digital librarian of the Internet Archive: “When people want to listen to music they go to Spotify. When people want to study sound recordings as they were originally created, they go to libraries like the Internet Archive. Both are needed. There shouldn’t be conflict here.”"

From the article

I believe they are arguing that the intent behind the digitization is fair use, as you say, but what I find interesting is they seem to argue that there is no loss of profit from their work, which is a valid point to raise - if this is all hypothetical exceptions can and should be made to the law.

Even if they don't have a case, say the copyright law is very tight and clear and there's no way this can skirt around it - they still can bring it to court, fight it, and lose until they get it overturned by the Supreme Court and they get a special status or the copyright law is amended. This is standard - it's how the 19th amendement was passed I believe, I'll look for a link.

Edit: to clarify, there is no damage to the copyright holders because the medium holding their work is impossible to be used to listen to their work by anyone but experts, like the IA

Edit 1: Here's what I was remembering - it's not an amendment, but it's neat!

https://lithub.com/how-ruth-bader-ginsburg-and-gloria-steine...