If it disgorges parts of NYT articles, how do we know this is not a common phrase, or the article isn't referenced verbatim on another, unpaid site?
I agree that if it uses the whole content of their articles for training, then NYT should get paid, but I'm not sure that they specifically trained on "paid NYT articles" as a topic, though I'm happy to be corrected.
I also think that companies and authors extremely overvalue the tiny fragments of their work in the huge pool of training data, I think there's a bit of a "main character" vibe going on.