The suppression of transverse phonons by liquidlike diffusion in superionic conductors has been proposed as a means to dramatically reduce thermal conductivity in thermoelectric materials [H. Lui et al. Nat. Mater. 11, 422 (2012)]. We have measured the ion transport and lattice dynamics in the original phonon-liquid electron-crystal Cu2Se using neutron spectroscopy. We show that hopping time scales are too slow to significantly affect lattice vibrations and that the transverse phonons persist at all temperatures. Substantial changes to the phonon spectrum occur well below the transition to the superionic phase, and the ultralow thermal conductivity is instead attributed to anharmonicity.