In many anime, characters that are supposed to be foreign (particularly English or American), it's clear that the seiyuu are Japanese because of the heavy accents. For example, Chris from Itazura na Kiss is supposed to be English, but her English has a thick accent and comes about as naturally as Naoki's (who is a native Japanese character).
But sometimes the English appears to be natural, such as in the opening scene for Eden of the East, where both the security guards outside the White House and the policy officer who questions Akira, seem to have no accent at all. Unfortunately, I was not able to find out if these were voiced by actual English speakers or just very skilled Japanese seiyuu because they were very small roles.
Do anime production teams hire native English (or other languages) speakers?