SOPA (officially) only addresses foreign sites. So they order removal from DNS servers and interrupt advertising or other funding processes from US based companies. But the ability to change the content on a server that is hosted in another country (I believe, IANAL) is beyond their capability. Someone please correct me if I'm wrong.
Also, the issue between domestic and foreign sites is still a bit vague in regards to SOPA. Supporters claim it only addresses foreign sites but most opponents claim (I think) that domestic sites can also be affected.
This is accurate, and a big reason why the EU officially passed a resolution against U.S. domain seizures.
All SOPA can do without infringing upon another country's sovereignty would be to remove the DNS entry on the U.S. servers that ties back to a foreign server, but they can't impact the foreign content itself without violating world law. The EU resolution strengthens that by saying that if the U.S. had hoped they'd be able to censor foreign content, the EU isn't going to just casually allow that to happen.
I would like to know as well but I think they are relying on the existing DMCA, which I think have similar provisions: domain seizures but no server manipulation.
AIUI the DMCA does not provide for domain seizures. Those are done under a creative interpretation of the property seizure laws that were written to allow the government to confiscate property used in the commission of a crime, (e.g. seizing and auctioning off cars that were purchased with drug money).
Also, the issue between domestic and foreign sites is still a bit vague in regards to SOPA. Supporters claim it only addresses foreign sites but most opponents claim (I think) that domestic sites can also be affected.