Anime production teams tend to hire native speakers of other languages to voice non-Japanese characters.
To use your example of Eden of the East. there are a number of English-language voice actors who are used for when it is set in America. For example, David Whitaker played the black man in the apartment in episode 1. Policeman A was played by Gregory Pekar, who has actually appeared in other Japanese movies/shows such as Hana Yori Dango, as well as American movies such as Lost in Translation.
These seem to generally appear in small roles and/or roles where they only speak English, such as the policeman.
