Does the Times believe that other people can get this text while it can't get it itself? To prove that the AI is stealing the info, Times does not need access to people's logs. All it has to show is that it can get that text.
This sounds like Citizen United again to AstroTurf and gets access to logs with a fake cause.
That logic makes no sense because if they don't get it right now then it does not mean that they will not get it in future.
If Times and its staff can get the text, is all that matters because the use and rate of data usage is not material as it can change any time in future.
Capone isn't allowed to burn his protection racket documents claiming he's protecting the privacy of the business owners who paid protection money. The Court can take steps to protect their privacy (including swearing the plaintiff to secrecy on information learned immaterial to the case, or pre-filtering the raw data via a party trusted by the Court).