What is the difference OpenAI has that lets them get away with, but not our hypothetical Mr. Smartass doing the same process trying to get around an NDA?
The user is "inputting variables into their probability algorithm that's resulting in the copyright work".
They tend to try argue for conspiracy to commit copyright infringement, it's a tenuous case to make unless they can prove that was actually their intention. I think in most cases it's ISP/hosting terms and conditions and legal costs that lead to their demise.
Your example of the model asking specifically "what copyrighted content would you like to download", kinda implies conspiracy to commit copyright infringement would be a valid charge.