"Knowing what Jennifer Lopez looks like" is a very distinct thing from "reproducing an exact replica" of training data. OP appears to be arguing that the former is not true because he thinks the latter is true, but it's actually the opposite. That's the crux of what I'm arguing here, OP is simply factually wrong about his position.

Edit: OP has pointed out that he doesn't actually think there are exact replicas being produced, which just makes this even more confusing.

Oh, it's a reference to that paper.

Firstly, that paper was written in January and examined a Stable Diffusion model that was already obsolete due to its poor training even back then. Secondly, even with that poor model they had to move heaven and earth to find a handful of examples out of hundreds of millions of training examples where they could get a blurry replica out.

Here's a Reddit thread from back in the day discussing how, really, this sort of thing just proves how difficult it is to do this.

Secondly, as mentioned, that model is long obsolete due to issues exactly like this. Modern models work better in part because they have better curated training sets that eliminate this sort of "overfitting." There's no indication in this article that the website in question is using one of those old models, it's just presented as a hypothetical concern.