Brillouin light spectroscopy (BLS) of polymers recorded much shorter relaxation times over the same temperature range than those obtained from other spectroscopies, including dielectric relaxation, dynamic light scattering, depolarized Rayleigh scattering, NMR, and molecular dynamics simulations. This is an anomaly because a priori BLS is thought to monitor the structural a-relaxation of polymers like all the other techniques. First noted in 1977, the anomaly was repeatedly confirmed, but it has not been explained, and it remains a puzzling finding in amorphous 8 polymers. In this paper, we explain this longstanding anomaly by the Coupling Model (CM), in conjunction with the fact that the alpha-relaxation of polymers is nonexponential at the relatively high temperatures of BLS measurements. The CM has the primitive relaxation, which is part of the Johari-Goldstein (JG) beta-relaxation, and the precursor of the structural a-relaxation. The calculated primitive relaxation times match the BLS relaxation times quantitatively. This indicates that the primitive relaxation together with the JG beta-relaxation of polymers is responsible for the phonon dispersion at hypersonic (GHz) frequencies, whereas the other spectroscopies probe mainly the a-relaxation. Additional support comes from the quasielastic neutron scattering experiment in the same polymer in which the primitive relaxation/JG beta relaxation was directly observed with relaxation times in agreement with the calculated ones as well as the BLS relaxation times. Thus, the longstanding anomaly of polymers observed by BLS now has an explanation.