If a person reads Tolkien, Herbert, Isaac Asimov, and then creates Star Wars, the things he or she read influence how they wrote Star Wars. There are things writing has given us over millennia, like story arc, character development, symbolism, etc. This is no different than an AI, learning from those who came before it, and using that knowledge to "take the next step". Tolkein likely read Orwell, who likely read... and so on and so fourth all the way back before Shakespeare.
You can own the copyright to a specific set of words creating your story. You can not own what your story inspires in others. Apply the same rules to AI. It is not a genie. It is just another creative entity using patterns and models like we do to do what until now only we have done.