A human makes their own choices about what to disseminate, whereas these are singular for-profit services that anybody can query. The prompt injection attacks that reveal the original text show that the originals are retrievable, so if OpenAI et al cannot exchaustively prove that it will _never_ output copyrighted text without citation, then it's game over.
> "[...] the fair use of a copyrighted work [...] for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include—
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work."
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So here we have OpenAI, ostensibly a nonprofit, using portions of a copyrighted work for commenting on and educating (the prompting user), in a way that doesn't directly compete with NYT (nobody goes "Hey ChatGPT, what's today's news?"), not intentionally copying and publishing their materials (they have to specifically probe it to get it to spit out the copyrighted content). There's not a commercial intent to compete with the NYT's market. There is a subscription fee, but there is also tuition in private classrooms and that doesn't automatically make it a copyright violation. And citing the source or not doesn't really factor into copyright, that's just a politeness thing.
I'm not a lawyer. It's just not that straightforward. But of course the court will decide, not us randos on the internet...