I don’t know. The public’s perception - encouraged by the AI labs because of copyright concerns - is that the outputs of the models are entirely new content created by the model. Search results, on the other hand, are very clearly someone else’s content. It’s therefore not unfair to hold the model creators responsible for the content the model outputs in a different way than search engines are held responsible for content they link, and therefore also not unfair for model creators to worry about this. It is also fair to point this out as something I neglected to identify as an important permutation of “safety.”
I would also be remiss to not note that there is a movement to hold search engines responsible for content they link to, for censorious ends. So it is unfortunately not as inconsistent as it may seem, even if you treat the model outputs as dependent on their inputs.