That may be true, but the white Appalachian can learn to switch accents/mannerisms (code switch). A black urbanite (who may already have had to learn to code switch, depending on where they grew up) can't change their skin color.
Yup, that is indeed a problem. 'Race' in the U.S. is, I believe, really a cypher for class, and where in other countries someone born to a lower-class can learn to fit in among a better class, it's impossible to change one's race.
This also hurts immigrants from other countries: they may be well-educated but on first sight they appear to belong to a lower class. It's very unfortunate.
There's also the reverse effect, notably lampooned in the film Love, Actually: if you've a British accent, Americans will assume you're posh.
