In 2006, Prochter et al. reported a statistically significant enhancement of very strong Mg II absorption systems intervening the sight lines to gamma-ray bursts (GRBs) relative to the incidence of such absorption along quasar sight lines. This counterintuitive result has inspired a diverse set of astrophysical explanations (e.g., dust, gravitational lensing) but none of these has obviously resolved the puzzle. Using the largest set of GRB afterglow spectra available, we reexamine the purported enhancement. In an independent sample of GRB spectra with a survey path three times larger than Prochter et al., we measure the incidence per unit redshift of >=1 ̊A rest- frame equivalent width Mg II absorbers at z ≈ 1 to be l(z) = 0.18 ± 0.06. This is fully consistent with current estimates for the incidence of such absorbers along quasar sight lines. Therefore, we do not confirm the original enhancement and suggest those results suffered from a statistical fluke. Signatures of the original result do remain in our full sample (l(z) shows an ≈1.5 enhancement over l(z)$_QSO$), but the statistical significance now lies at ≈90% c.l. Restricting our analysis to the subset of high-resolution spectra of GRB afterglows (which overlaps substantially with Prochter et al.), we still reproduce a statistically significant enhancement of Mg II absorption. The reason for this excess, if real, is still unclear since there is no connection between the rapid afterglow follow-up process with echelle (or echellette) spectrographs and the detectability of strong Mg II doublets. Only a larger sample of such high- resolution data will shed some light on this matter.