OpenAI is taking the position similar to that if you sell a cook book, people are not allowed to teach the recipes to their kids, or make better versions of them. That is absurd. Copyright law is designed to strike a balance between two issues. One the one hand, the creator’s personality that’s baked into the specific form of expression. And on the other hand, society’s interest in ideas being circulated, improved an…
Just to play devil's advocate, OAI can argue that they spent great effort creating and procuring annotated data. Such datasets are indeed their secret, and now DS gets them for free by distilling OAI's output. Besides, OAI's EULA explicitly forbids users from using the output of their API for model training. I'm not saying that OAI is right, of course. Just to present OAI's point of view.
However, OpenAI and Google are far more politically influential than the lobbyists in the 90s, so it is likely to succeed.