The Walking Dead is another example. That said I don't hear the connection. I hear a lot of native Southerners in the course of the day here in Georgia, and they don't sound British to me. Yes, I have lived there too.
That's because the Southern accent is more tonal. When I was in Egypt, everyone I met thought I was British.
Are you trying to tell me that most people born and raised in the Appalachians aren't of Scottish descent, and their dialect isn't influenced as such?
No, they're not. They're Scots-Irish (along with English, German, and a little of everything else), and Scots-Irish are a completely different group that spoke a northern English dialect. About 10 percent of Americans can trace their family all the back to the American Revolution on both sides of the family. About half of those live in Appalachia. To trace that accent back, I'd look at where the Scots-Irish were before they moved to Ulster and then on to Americ. accents in Ayr, Stranraer, Wigtown, but those have shifted some since then with influences from the north plus normal changes.
What Chup said. It's not simplified, just a bit different. A biscuit describes two different types of food depending if the speaker is American or British. And American say "I spent the entire Monday..." while Brits will use "I spent the whole of Monday..." The same thing happens with Spain Spanish versus Mexican Spanish and the two communities that speak Portugues.