The pitch-angle distributions of solar energetic particles (SEPs) provide a wealth of information about particle transport through interplanetary space, and depend on the magnetic field strength, topology, and turbulence at remote heliospheric locations. The Low Energy Telescope (LET) on STEREO measures angular distributions in the ecliptic for SEP ions from protons to iron with energies of about 2--12 MeV/nucleon. At the onset of the 23 July 2012 extreme SEP event, a beamed distribution was observed at STEREO-Ahead using LET. We have previously reported apparent "oscillations" in the pitch-angle width of this beam when using simultaneous particle and magnetic field measurements at a 1-minute cadence. We have now determined that this behavior is largely a result of the effects of magnetic turbulence on the calculated particle pitch angle distributions. The locally measured magnetic field direction varies relatively rapidly, while the energetic particle distribution is governed by magnetic fields averaged over much larger spatial and temporal scales than represented by solar wind measurements at the same cadence. Similar behavior in earlier events has been reported by others and analyzed in the framework of quasilinear theory.