Everybody seems to be focused on whether or not the OpenAI copied the data in training, but my understanding of copyright is that if a person when into a clean room and wrote an new article from scratch, without having read any NYT, that just so happened to be exactly the same as an existing NYT article, it would still be a copyright violation.
As soon as OpenAI repeats a set of words verbatim, it violates copyright.
The courts should examine how much damage an occasional verbatim regurgitation would damage NYTs business. (I would guess not much)