No, what Gelman says is that he suspects that to compensate for the fat tails in 538's state distributions, they had to reduce the between-state correlations, to get a desired overall level of uncertainty.
This implies that correlations increase, rather than decrease, the overall level of uncertainty.
This is also easy to see from a basic probability perspective, using the concept of variance. For example, if you have two coin flips, with outcomes {-1, +1} chosen uniformly at random, then the sum has variance 2 if the flips are independent, but variance 4 if the flips are perfectly dependent.