Beat me to it.
I have no clue what the author means by an American accent. Cross state lines, or for that matter from inner city to suburbs, and you're listening to a different accent.
The reference in the article about the upper classes adopting the non-rhotic speech makes me think of NPR. Why do they use so many people with “British” accents? Do they think it lends credence to their propaganda?
You hear it, but I bet they don't. I know people from Belfast, Ireland, who swear they can tell the difference in accent from neighborhood to neighborhood and sometimes even street to street. I can tell the difference from parts of Scotland, and different parts of Ireland, but that's about it.