Nobody disputes that I own the copyright in a sound recording I made just by pushing the red button on my recorder. So it is a mystery to me that copyright to any sort of human conditioned machine generation is in dispute.

The sound recording analogy breaks down at the point where the recorder makes no creative decisions. Pressing record captures what is already there. Prompting Claude generates something that did not exist, through decisions the model makes about structure, naming, pattern, and implementation. The closer analogy is hiring a session musician and telling them the key and tempo. You own the recording under work-for-hire if they signed the right contract, but the creative expression in the performance is theirs unless explicitly assigned. The button you push to start the model is not the same button as the one on the recorder.