When I hear the same person speaking, I hear a decidedly British inflection.
In one of the posts a writer refered to Dan Rather as having a midwestern accent. Typically we in the US view midwestern accents as being neutral. However a British native would immediately pick up on the midwestern accent.
The French have a lovely lyrical sound when speaking English, the Germans sound gutteral to me. Those from India have a distinctive sound as do people from the Japan and the South Seas.
I love to hear people from other countries speak English and enjoy the addition of sounds to the English language that other languages can add.
I think that neutral accent is in the ear of the beholder.