Without taking a stand on whether this _should_ be illegal or not, but whether it _is_, I could imagine that a legal system might want to give the painter a way to get income for a limited time by distributing copies of the painting, and that copying it in this way would infringe upon those rights. In this case though, I'd argue that the modern analogue of this would be Robin Hood getting invited over to watch a movie with the noble (which would be allowed!) and then secretly burning a copy of the DVD when the noble went to the bathroom. Our current legal system doesn't consider "I didn't know what I was doing was illegal" to be a valid defense, so Robin Hood would still be committing a crime by sharing the DVD further after he's copied it. (Since we don't have genies in real life, I don't know how the law would consider them culpable, but based on my very limited knowledge of genie lore, my guess is that the amount of free will they have in this situation is about the same as the DVD burner, so they probably would be okay from the perspective of the law?)
Interestingly, I think that the more direct analog to what we have today would be if the noble themself had the genie copy the painting and gift it to their friend Robin Hood. I do think the same logic I gave above ultimately applies to whether our current legal system would allow the artist to enforce exclusivity, but I find it a lot more compelling as an argument about whether it _should_ be allowed or not compared to the hypothetical you gave. In your version of it, it doesn't feel like allowing what Robin Hood did is particularly beneficial to society, but in the version where the noble is an enthusiastic participant in the copying, it seems a lot more like outlawing it would lead to some harmful dynamics (like you mention about whether the noble bears responsibility for protecting access to the painting based on obtaining it). In other words, having a system where the artist is allowed to enforce his exclusive distribution rights universally actually seems _less_ problematic to me at first glance than one that only applies to those who sign an agreement when purchasing the paintings.
To put this in terms of torrenting, my naive understanding is that right now, it's definitively considered illegal to seed protected content, and the question is whether it's legal to download it without seeding or not. I actually think that it would be worse to allowing downloading without allowing seeding as well, so the system that Meta is arguing for would be worse than if what they did is also illegal. However, I'm honestly not sure if they're actually right or not about what the law says, and that's why I brought up the hypotheticals I did. I also honestly don't feel confident in my feelings on whether I'd prefer to ban both seeding and downloading protected content or to eliminate the legal protections entirely and allow both, but it doesn't seem like that's actually the legal question at the heart of the current matter.