The is a bar of usage built into the law, otherwise everyone who reads this wired article is violating copyright by making a full copy to their computer. Generally making non-lasting copies is fine, otherwise the internet wouldn't work.

AI doesn't need lasting copies to train, however I don't know what the actual implementation is. But if it's ruled that they can only use copyrighted data if it's not stored for more than the time it would take a human to consume, It wouldn't really cripple the models, but perhaps make training more logistically challenging.

It's important to understand that models are not data archives. They are statistical constructs made from getting quizzed, that uses human made content to generate the quiz questions.