As a counter argument it might be reasonable to instead say that the NYT delivers "current information" so perhaps it'd be fair to train your model on articles so long as they aren't too recent... but I think a lot of the information that the NYT now relies on for actual traffic is their non-temporal stuff - including things like life advice and recipes.
This isn't even "fair use". The ideas in a work are simply not protected by copyright, only the form is.