To be honest, I'm a little perplexed.
I don't know enough about the demographics of the counties that you are talking about.
I do know that Carter swept the south in 1976, and lost close races to Ronald Reagan in most of the southern states in 1980. 1980 was the last election in which the Democratic percentage of the vote was higher in the south than in the rest of the country.
I don't know what percentage of the black vote Ford and Reagan got in 1976 and 1980, respectively, though I don't think blacks ever had the hostility to Ford that they did to Reagan. And Ford had basically written off the south, and had not made what anybody would consider to be under-the-table appeals to white racist voters in the south.
So it could be that while Ford surely fared poorly among blacks, he didn't do as poorly as Reagan did, and that in heavily black areas, Carter could have improved his overall showing, even though his performance among white voters slipped badly between the two elections.