Lack of dispersion cancellation with classical phase-sensitive light

J.H. Shapiro recently argued that nonlocal dispersion cancellation using entangled pairs of photons is essentially classical in nature, based on a comparison with a classical model in which two stationary, chaotic beams of light have phases and frequencies that are anti-correlated, which he refers to as "phase-sensitive" light (arXiv:0909.2514). It is shown here that there is no physical cancellation of dispersion for classical light of that kind, and Shapiro's results merely reflect the fact that identical dispersion occurs in both beams. The origin of the cross-correlations between the intensities of the two beams is shown to be completely different in the classical and quantum-mechanical cases.