if you take any piece of art someone else created, and you use it to make your own stuff without their authorization, you're committing a crime.

This is not accurate. No art is made in a vacuum; all artists are influenced by other art. That's even before we bring in fair use, which may or may not apply depending on specifics.

Copyright does not restrict who/what can be trained on copyrighted works. That's just not a real thing. It's becoming an issue because AI is rapidly becoming "good enough" that human artists are worried they will be replaced, so they're scrambling to find a way to hold back technology. This happens every time a new technology is used in reference to media. Every. Single. Time. It never works.