Huh? Not really, internet shutdowns are a documented and real thing. Suggested reading (all of which refer to the internet as being shut down or blacked out): [0] [1] [2]
The fact that you need to connect to the internet through a service provider plus mostly-centralized control of infrastructure like DNS or BGP means shutting down the internet is a real thing that has been done several times. It doesn't happen in the developed world because their service economies are so highly dependent on internet connectivity, but if e.g. the US government had to contain a theoretical rogue escaped AI, they could absolutely get ISPs to metaphorically unplug the network cable and take down the internet as we know it.
[0] https://en.wikipedia.org/wiki/2026_Internet_blackout_in_Iran
[1] https://en.wikipedia.org/wiki/Internet_in_Egypt#2011_Interne...
[2] https://www.reuters.com/world/india/india-asks-telecom-compa...