North Korea likely has a very small number of connections to the internet. Take out 1 or 2 switches and they go down. The US has thousands. We are vulnerable but not the internet as a whole.
The targets would be focused on mostly critical areas which would cause the most damage. In fact some of our most sensitive networks have already been compromised, some repeatedly. To the point where they were all but shut down due to those intrusions. There are many ways to shut down and or cripple large sensitive communication networks. But you're free to believe that thing about switches.