For Access Copyright, if you go to their submissions and to their documents, they say that you can copy every published work, except specific works that appear on an exclusion list. In order for it to appear on an exclusion list, someone has to actively tell them, “Take me out.” That's how they structure their business.
This is not how the law works. The way the law works is that they can only license works when the copyright owners authorize them to act on their behalf. That's how they work.
Now, if you want to read more about what the Copyright Board said about the repertoire most recently—I think it was the 2015 K-to-12 tariff—there is a rather extensive discussion on the repertoire and lack thereof, and why it would be infringement to authorize things they don't have. I think that's the latest thing the Copyright Board said about that.