I'm not sure if Carter won the white vote in Kentucky/Tennessee.
For one, those historically were the most Republican of the southern states, Tennessee moreso than Kentucky.
Kentucky was a union state for a reason, so yeah.
And Eastern Tennessee has always been a Republican stronghold. The place voted for Lincoln! Tennessee was always Democrat-leaning, but in good years, Republicans could take the state. The rest of the South usually wasn't like that.
Kentucky was 7.8% black in 2010, so we can safely assume that it wasn't that different (probably less) in 1980. If only 1000 Kentuckians voted then they would roughly split as 527 to 456. Even if we say 80 of these 1000 are black (ignoring turn out etc) and we have them voting 80% Carter that still leaves Carter winning the remainder 463 to 440. Basically there weren't/aren't enough blacks in Kentucky to change anything.
Actually yeah, looking at that, you're right. Kentucky whites voted for Carter, interestingly enough.
Looking at the results in Tennessee, Carter might have pulled it out there as well, which seems remarkable.