"Doesn't she also remind you of Al Gore with his "accent" which he puts on when he talks to black people? Ick, that's embarassing."
George Bush does exactly the same thing. He drops "g's" more and his accent gets thicker when he's talking to the general public. He's more "refined" sounding when he's talking to executives or some similar group.
The reality is that we all do it to some degree. Even if you don't change your accent you change the way you talk to people based on your perceptions of them. I know I do in my job. And I do it because it works.
Given everything else, this is a pretty silly thing to spend any time on.
As you concede, it does provide insight into the speaker's view of his audience, which, In the case of the clintons and Gore, is, invariably, haughty disdain.