I am in the middle of a DMCA request, as I have found someone who is using some of my copyrighted content. The host is based in China, and is not responding to any requests (I have sent faxes, e-mails, and a letter).
Now, as far as I was aware, it is possible for a domain registrar (the domain is registered via Network Solution) to take down a domain by changing or destroying the name server entries.
Is the assumption in the above paragraph correct?
Yes, you are correct the name server provider could take the domain offline by removing the zone information.
There however would be nothing stopping them from registering the domain again with another registrar either in the US or another country making you go through this all over again.
Their legal division may, or may not, want to get involved depending on their interpretation of safe harbor provisions -- Section 512(c)(1). I would recommend reading through them yourself, or ask your lawyers, for an opinion on the matter.