Offshore server is often used to host or promote things that are illegal, prohibited or prohibited in their home country. For example, Poker and casino are banned in India and other Asian countries and to host these websites/content, an Asian customer has no choice but to get Offshore hosting.
The best example of this is the website named WikiLeaks. WikiLeaks makes public US government secret documents. WikiLeaks uses Offshore hosting service located in Sweden. The US would have shut down this website instantly if it had not used no DMCA server. Since Sweden is an advanced country in terms of press freedom, there is no reason to close WikiLeaks.