That would be like me just photocopying a book you wrote and then handing out copies saying we’re assigning different rights to the content. The whole point of the lawsuit is that OpenAI doesn’t own the content and thus they can’t just change the ownership rights per their terms of service. It doesn’t work like that.
In any case, the point is that they made no claim to Output (as opposed to their code, etc) being their IP.
By your logic, Firefox is re-distributing content without permission from the copyright owners whenever you use it to read a pirated book. ChatGPT isn't just randomly generating copyrighted content, it just does so when explicitly prompted by a user.
Of course, if the input I give to ChatGPT is "here is a piece from an NYT aricle, please tell it to me again verbatim", followed by a copy I got from the NYT archive, and ChatGPT is returning the same text I gave it as input, that is not copyright infringement. But if I say "please show me the text of the NYT article on crime from 10th January 1993", and ChatGPT returns the exact text of that article, then they are obviously infringing on NYT's distribution rights for this content, since they are retrieving it from their own storage.
If they returned a link you could click, t and retrieved the content from the NYT, along with any other changes such as advertising, even if it were inside an iframe, it would be an entirely different matter.