This is true, but you could also say the same about the phrases "English accent" and "Scottish accent" -- a Scouse accent sounds nothing like RP, and a Highland lilt is very different from the accent in the Gorbals.

And the Appalachian accents of Justified sound very different to the Mid-Atlantic accent of Frasier Crane -- yet to me, as an outsider, there is still an indefinable "Americanness" common to them all.