I can understand the gut reaction of "how dare they?!" but upon deeper consideration... it's not really a big deal. These networks don't regurgitate content, they synthesize new content. Even if someone generates art in the style of another artist, it won't spit out that artist's work, only imitate their style -- so as long as the person doesn't claim it's the other artist's work, it's not different from one artist taking inspiration from another's work.
As far as the legal argument of "I didn't give permission to train the network on my work" goes... I think that's shaky at best. These AIs are trained on publicly available data. Training an AI is basically just showing it stuff to learn from, and as such it's a bit like suing because "I didn't give this art teacher permission to show his class my publicly-available painting during a lesson!" Which I don't think you could argue legally (though I'm not a lawyer, so maybe you can).
The USA, and indeed the entire western world, has let the concept of "ownership of an idea" gradually take over copyright, trademarks, patents and other "intellectual property". I think we'll be stuck with lawsuits about how close an algorithm can come to something like "an artist's signature style", beginning in the near future. Laws will be proposed with lots and lots of really terrible follow-on effects, and sooner or later, one of them will pass.
As far as the legal argument of "I didn't give permission to train the network on my work" goes... I think that's shaky at best. These AIs are trained on publicly available data. Training an AI is basically just showing it stuff to learn from, and as such it's a bit like suing because "I didn't give this art teacher permission to show his class my publicly-available painting during a lesson!" Which I don't think you could argue legally (though I'm not a lawyer, so maybe you can).