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.