No, they can't. The rest of the world would just route around the US with BGP. All of the US infrastructure/service providers would be down, so a ton of things would break, but the Internet would not be "shut down". The US government also no longer has authority over the DNS root servers. So unless you're referring to thermonuclear war or some similar scenario then the US does not have this capability.
They are throwing numbers out like “10%”.
If they are serious and believed then yes, prepare for the possibility of very extreme reactions at a global and potentially nuclear scale.
World Wars flattened cities all over the world for much less.
We can’t talk about AI being the end of the species and not expect the most extreme reactions in global History.
Or maybe we just put some nerds who cant control their agents and keep running their mouths in jail?
For example, there’s one building in Seattle that would cause region-wide problems if it was knocked offline.