I don't have a comment on your hypothetical, but this case seems to go far beyond that. If you read the actual filing at the bottom of the linked page, NYT provides examples where ChatGPT recited exact multi-paragraph sections of their articles and tried to pass it off as its own words. Plainly reproducing a work is pretty much the only situation where "is this copyright violation?" isn't really in flux. It's not dissimilar to selling PDFs of copywritten books.
If NYT were fully rellying on the argument that training a model in wordcraft using their materials is always copyright violation, or only had short quotes to point to, the philosophical debate you're trying to have would be more relevant.