Do rotations beyond the cosmological horizon affect the local inertial frame?

If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results for the dragging of inertial frames in closed, flat, and open universes with and without a cosmological constant.