Nope. DALL-E generates images with the Getty Watermark, so clearly there’s copyrighted materials in its training set: https://www.reddit.com/r/dalle2/comments/xdjinf/its_pretty_o...
So even if we’re assuming these were wholly original works that the author placed under something like a Creative Commons license, the fact that it incorporated an image they had no rights to would at the very least create a fairly tangled copyright situation that any really rigorous evaluation of the copyright status of every image in the training set would tend to argue towards rejecting as not worth the risk of litigation.
But the more likely scenario here is that they did minimal at best filtering of the training set for copyrights.
I agree with you that it is also possible that people posted Getty thumbnails to some sites as though they are public domain, and that is how the AIs learned the watermark.
Not a lawyer, of course, but I think slapping the Getty logo on a work claiming "fair use" and then releasing the work under public domain would be a case of misrepresentation, because Getty still has a copyright claim on your work. Regardless of the copyright status, it's still a clear trademark violation to me.
Obviously, that would not entitle anyone to rip those elements from your work and use them in a way that was not fair use. The Getty watermark could fall into this category: public domain pictures using the watermark fairly (for transformative commentary/satire purposes) could go into the network, which uses that information to produce infringing images.
Trademarks are a different story, but trademark protections are a lot narrower than you might think.
The point is that it's very conceivable that the neural network is being trained to infringe copyrights by training entirely with public-domain images.