So I'll add a question. Could they try to defend their IP in courts against downstream consumption by other models, while simultaneously ignoring their hypocrisy? I mean... of course they can. I withdraw my question.
They aren't claiming a copyright violation, they are claiming a contractual violation - that Deepseek violated the terms of use of their API by allegedly using the API to generate training samples.
People who don't like OpenAI are trying to claim copyright violations that OpenAI 'stole' copyrighted works. Under US law there is 'transformative fair use' - and machine learning models are pretty clearly transformative. So they aren't really the same thing, since in this case copyright isn't being asserted, just a contractual violation.
Now, if a third party had generated the content with the API and published the generated content. Then DeepSeek downloaded and trained on that content, then neither the third party nor DeepSeek would have done copyright violation nor Terms of Use violation.