If using data from those websites in a way decreases their visitors or something similar then I think there's an argument to be made for that. I don't know the details to case but just because something is publicly visible doesn't mean that you can just do anything you want with it.
Every major news site in Europe is full of articles full of "The New York Times reported that [summary]" so I'm a bit confused as to why, all of a sudden, it's a problem.
Newspapers have been doing this for at least a century, while news radio and news broadcasts have done it since their inception.
There is no guarantee that a website would get a visit if there was no AI summary. Also you can do anything you want with public domain information. That's the whole point of it being public. Otherwise it should be licensed or copyrighted content.