You're not correct. There are accents strong enough in both SC and the UK to befuddle the other. Heck, even within SC it'd be hard for some northern transplants to understand rural drawls, and within the UK it's not unknown for Londoners to wonder at Glaswegians (https://www.youtube.com/watch?v=91Tj7eezFJ8).
I don't know about that. I had difficulty understanding people from different parts of my own home state (Kentucky). I grew up in the Louisville area, and had difficulty understanding people from the eastern part of the state.
I have also had severe difficulty understanding some of my wife's family, who are from Maine.
And now I work with many people from the UK. I tend to find that if the person is from the south, I have few problems understanding them. The further north someone is from, the more difficulty I have with them. Some of my Scottish coworkers are, for me, almost impossible to understand.
I've had similar experiences. I once encountered a somewhat drunk Acadian man when I was in Texas. It was several minutes before I figured out that he was, in fact, speaking English.
Years after they left Georgia, my parents still liked to tell us about the time they were introduced to bald eggs: the third time the waiter asked very slowly, "Would you like some boiled eggs?"
I was born in Philadelphia and now live in Atlanta. Once while driving from Atlanta to Athens I picked up on the radio a man talking about how everyone should come down to the Wal-Mart parking lot and have some "bull penis". I knew that couldn't be what he was saying... it turned out he was talking about "boiled peanuts".