Except, you're wrong. That's not how it works. It's dependent on 13 servers, that route the entire internet. These hackers took out 7 of said servers.
And no, they weren't doing this from one station. They have been working with Trojan Viruses for several years, to create "Zombie Computers," which run normally except when the hackers tell them to do something via the Trojan. So, while they're waiting for their commands to send packets and such, they'll be uploading spyware or spambotting websites and forums, etc.