This is literally what's happening here. No one is cutting off the admin's personal Internet connection to get on the Internet. They're taking his website down because it's full of abuse.
They're cutting off the company's internet connection, which isn't significantly better than a personal connection. The entity doing this is not the web host, it's the ISP. I would be fine with a web host refusing service, but that is not what is happening.
I think website hosts should be able to drop people for most reasons, but that's not what's happening here