That's not what the study says. What the study says is that people in general in the US perceive Southerners to be less well off and less well educated than people who aren't from the South.
The person who ran the study is from the South, but doesn't have the accent. She says that because people tend to stereotype you, that she turns it off. She still has it when with extended family, but not general conversations.
I thought the study was interesting. Since I'm from the South and have lived in the North and Midwestern states, my accent tends to be a mish-mash. When I speak with my original accent, it is hard core West Texan, which anyone from NC would decry as an abomination. (I know, I went to junior high there and got days of harassment for my pronunciation of “nice white rice”.)
I found it disconcerting that a Southern accent implied such negative things to people.