Except, in copyright law it depends on the _input_.
These models would not exist if they were not first fed the source material.
Until we have systems that are not trained on a pre-existing corpus this will remain true. No matter how clever the algorithm, without the source material you have no output. Zilch. Nada.
Now, when the source material is someone else's property this means that without - someone else's property - you would have had no output.
So, when you want to use someone else's property, which you do not own, the general rule is that you a) first ask them if you may and b) pay them for the right to use their property.
In this sense it is no different than using a photocopier.
It's the copyright ownership of the material you put into the machine that will interest the judge not the quality of the copy.
I'm really looking forward to the first court cases and predict that much hilarity will ensue!