Yup. Violating IP licenses is a great reason to prevent it. According to current law, if they get Alice license for the book they should be able to use it how they want.
I'm not permitted to pirate a book just because I only intend to read it and then give it back. AI shouldn't be able to either if people can't.

Beyond that, we need to accept that might need to come up with new rules for new technology. There's a lot of people, notably artists, who object to art they put on their website being used for training. Under current law if you make it publicly available, people can download it and use it on their computer as long as they don't distribute it. That current law allows something we don't want doesn't mean we need to find a way to interpret current law as not allowing it, it just means we need new laws that say "fair use for people is not the same as fair use for AI training".