I think the characterization is unfair to generative AI, because the information that is retained in the model is a very lossy and rough generalization of the training data - that situation is a lot less direct than what it's like with search engines. In my mind, the lawsuits against search engines have a lot more ground to stand on. Saying that something "provides access to copyrighted content" almost implies that there's some mechanism that allows the user to wholesale download complete, unedited and exact copies of some copyrighted material - I could see that argument with a search engine, but not really with a text or image generator.