To shuck and jive" originally referred to the intentionally misleading words and actions that African-Americans would employ in order to deceive racist Euro-Americans in power, both during the period of slavery and afterwards. The expression was documented as being in wide usage in the 1920s, but may have originated much earlier.
"Shucking and jiving" was a tactic of both survival and resistance. A slave, for instance, could say eagerly, "Oh, yes, Master," and have no real intention to obey. Or an African-American man could pretend to be working hard at a task he was ordered to do, but might put up this pretense only when under observation. Both would be instances of "doin' the old shuck ‘n jive."
Those people are half right: Carney wasn't a racist when he said it because he was talking about himself. Palin, however, is purposely aiming slave-owner terminology at a black person.
Therein lies the racism.