Contrast this with Apple's case where it looks like they've got evidence of people walking out of the building with various physical artifacts on their way to an OpenAI interview.
Also, more seriously, there are plenty of pieces of information that are compelled to be published that don't lose their confidentiality. There actually is a general concept that confidentiality can be lost if you are negligent in its protection but it's a very nuanced thing.
The copyright office's recent statement on this matter were sensationalized when they really said nothing groundbreaking at all -- this was always the standard applied when any tools are used in creating a work.
Ultimately it all hinges on the specifics of the training and how much human involvement was involved throughout the creation process. I suspect arguing this successfully in favor of upholding a copyright would be an uphill battle for many situations, but ultimately we'll need more court cases to know for sure.