The rich statistics of galaxy rotations as captured by the velocity function (VF) provide invaluable constraints on galactic baryon physics and the nature of dark matter (DM). However, the comparison of observed galaxy rotations against cosmological models is prone to subtle caveats that can easily lead to misinterpretations. Our analysis reveals full statistical consistency between ∼5000 galaxy rotations, observed in line-of-sight projection, and predictions based on the standard cosmological model (ΛCDM) at the mass-resolution of the Millennium simulation (H I line-based circular velocities above ∼50 km s-1). Explicitly, the H I linewidths in the H I Parkes All Sky Survey (HIPASS) are found to be consistent with those in S 3-SAX, a post-processed semi-analytic model for the Millennium simulation. Previously found anomalies in the VF can be plausibly attributed to (1) the mass-limit of the Millennium simulation, (2) confused sources in HIPASS, (3) inaccurate inclination measurements for optically faint sources, and (4) the non-detectability of gas-poor early-type galaxies. These issues can be bypassed by comparing observations and models using linewidth source counts rather than VFs. We investigate if and how well such source counts can constrain the temperature of DM. © 2013. The American Astronomical Society. All rights reserved.