The bright WN4 star EZ CMa exhibits a 3.77 d periodicity in photometry , spectroscopy , and polarimetry , but the variations in the measurements are not strictly phase-locked, exhibiting changes in reference times, amplitudes, and the shape of the variability happening over times as short as a few weeks. Recently, 137 d of contiguous, variable photometry from BRITE-constellation was interpreted as caused either by large-scale dense wind structures modulated by rotation, or by a fast-precessing binary having a slightly shorter 3.626 d orbital period and a fast apsidal motion rate of 1315(degrees) yr( -1). We aim at testing the latter hypothesis through analysis of spectroscopy and focus on the N V lambda 4945 line. We derive an orbital solution for the system and reject the 3.626 d period to represent the variations in the radial velocities of EZ CMa. An orbital solution with an orbital period of 3.77 d was obtained but at the cost of an extremely high and thus improbable apsidal motion rate. Our best orbital solution yields a period of 3.751 +/- 0.001 d with no apsidal motion. We place our results in the context of other variability studies and system properties. While we cannot fully reject the precessing binary model, we find that the corotating interaction region (CIR) hypothesis is better supported by these and other data through qualitative models of CIRs.