Anyone with access to the NYT can also just copy paste the text and plagiarize it directly. At the point where you're deliberately inputting copyrighted text and asking the same to be printed as an output, ChatGPT is scarcely being any more sophisticated than MS Word.
The issue with plagiarism in LLMs is where they are outputting copyrighted material as a response to legitimate prompts, effectively causing the user to unwittingly commit plagiarism themselves if they attempt to use that output in their own works. This issue isn't really in play in situations where the user is deliberately attempting to use the tool to commit plagiarism.