Are rotating planes of satellite galaxies ubiquitous?

We compare the dynamics of satellite galaxies in the Sloan Digital Sky Survey to simple models in order to test the hypothesis that a large fraction of satellites co-rotate in coherent planes. We confirm the previously-reported excess of co-rotating satellite pairs located near diametric opposition with respect to the host, but show that this signal is unlikely to be due to rotating discs (or planes) of satellites. In particular, no overabundance of co-rotating satellites pairs is observed within $\sim 20^{\circ}-50^{\circ}$ of direct opposition, as would be expected for planar distributions inclined relative to the line-of-sight. Instead, the excess co-rotation for satellite pairs within $\sim 10^{\circ}$ of opposition is consistent with random noise associated with undersampling of an underlying isotropic velocity distribution. We conclude that at most $10\%$ of the hosts in our sample harbor co-rotating satellite planes (as traced by the luminous satellite population).