As an explanation for the rust-belt as a whole that seems inaccurate; the south today is not nearly as industrialized as the northeast was in its heydey. Certainly the steel industry, one of the dominant industrial sectors, has not moved to the southeast, which has almost no steel industry; it's done a mixture of just shutting down entirely, and moving to China. The automotive industry is closer to being accurate, though I don't think the number of automotive jobs created in the southeast is actually particularly large, certainly nothing on the order of the change in Detroit's population.