Isn’t your brain doing the same thing when it reads text or views a painting? Some people can even memorize and precisely recreate the things they’ve seen. But no one considers the process of lossy storage in human memory to be copyright infringement. Instead the later reproduction itself might be infringing. I think it will be the same here. Training models on copyrighted content won’t fall afoul of any existing law, instead legal challenges will have to be aimed at specific instances where the models produce output that arguably infringes copyright.
That’s inconvenient for opponents of this technology because they would prefer to ban the training itself, but there’s not a good justification under existing law to do this.