Not sure about US or other jurisdictions, but that's not how any of this works in Germany. In Germany downloading anything from anywhere (even a movie) is never illegal and does not require a license. What's illegal is publishing/disseminating copyrighted content without authorization. BitTorrenting a movie is illegal because you're distributing it to other torrenters. Streaming a movie on your website is illegal because it's public. You can be held liable for using a photo from the web to illustrate your eBay auction, not because you downloaded it but because you republished it.

OpenAI (and Google and everyone else) is creating a publicly-accessible system that produces output that could be derived from copyrighted material.

I think it works like that in Canada and some other places too, because they pay an extra tax on storage media when they buy it, which essentially authorizes a license for any copyrighted material that might be stored on that media.

> In Germany […]

That‘s confidently and completely wrong.