If there's a specific prompt that makes the model produce such an image (without img2img), why shouldn't it count? The question isn't whether the model produces such things randomly, but rather whether it's capable of producing them in principle, even if it requires a very elaborate prompt.
> If there's a specific prompt that makes the model produce such an image (without img2img), why shouldn't it count?
There's a specific prompt which makes a human artist produce such an image without img2img too: "Please draw the Mona Lisa". There - you just did it in your head while reading this comment!
So? Humans aren't copyrightable works. But a bunch of weights that constitutes the model is just data, and that data can very well contain copyrighted works. The question is whether it does in any meaningful sense. And if it can reproduce them verbatim with the right prompt, I don't see how the answer could be "no", anymore so than a password-protected archive of a copyrighted JPEG.
But you certainly can get things like watermarks without any real memorization. Watermarks have been a nuisance in GANS, for example - the StyleGAN CATS model was filled with watermarks or attempted meme text captions, even though the cats were so nightmarish that they obviously weren't 'plagiarized' so nobody made a big deal about it back then and they understood the GAN had simply learned that watermarks were a thing in many real images and it would try to imitate them where plausible in a sample.