You are allowed to read books from the library and remember what they say, and use that information to inform your own future writing or speaking or actions.
You are allowed to listen to copyrighted music and learn from it. You can even play songs from The Beatles or Metallica in your garage as training.
You absolutely do have the right to "train your brain" on copyrighted material. Copyright restricts who is allowed to publish the work, not who is allowed to consume it.
You could count the words in a book and publish the word count, and while the information is based on the contents of the book, that would fall incredibly short of being a derivative work.
I suspect they committed whatever copyright violation is committed when they downloaded the copyrighted works. Training an AI on them is simply not related to the protections that copyright offers.
You aren't allowed to download a torrent of pirated books as these companies have done and freely distribute it to multiple brains to train on.
If the brains can then write down the original works from memory, you aren't allowed to make copies of these brains and freely distribute them either.
The syntax brought to mind Stephen Colbert's 2007 book, I Am America (And So Can You!)