> It's just that the owner of the training set -- not the owner of the algorithm -- is the one with the valid claim to copyright.
Not all that different from a pop song made by editing together licensed samples, no?
In that case, the song is certainly a derivative work of the samples, and so the producer of the song needs to get derivative-works-allowed licensing from the samples’ authors (which is what you must necessarily get when buying samples from a sample library, for them to be of any use at all.) The produced song is then its own work with its own copyright. Sometimes, larger samples (like reused vocal performances) require payment in, essentially, “equity”—a percentage of the song’s royalties are transferred as royalties to the sample. But in most cases, the sample is purchased for a flat fee, and there is no ongoing relationship between the revenue of the song and the revenue of the sample.
Is anything different if you replace “song” with “news article” and “samples” with “training set”?