Pirated content is already available in US and other countries via thepiratebay and other torrents sites. Pirating copyrighted content is already considered illegal in the US, and is being actively monitored by media companies. If this Antiguan website indeed becomes accessible to Americans, or say other country, how will downloading from this site differ from downloading via torrents. Since torrent usage is already being monitored in US, there's a high likelihood that American ISPs would monitor the usage of this site as well.
Edit: Downloading copyrighted content -> Pirating copyrighted content.