In the present work, a tentative suggestion as to the cause of the well-known discrepancies among the slopes of the several available calibrations of the absolute magnitude of the horizontal branch (HB) at the color level of the instability strip as a function of metallicity is advanced. This is based upon the combination of two effects: 1) the significant deviation in luminosity of the RR Lyrae variables from the ZAHB locus at low metallicities and blue HB morphologies, as suggested by recent synthetic HB (SHB) calculations; and 2) the observed increase in the HB luminosity "thickness" DELTA-M(V)(HB) with increasing cluster metallicity. If these two effects are taken into account, a semiempirical scenario may be constructed which suggests that the slope alpha(LE) of the absolute magnitude-metallicity relation, as derived using the lower envelopes (LEs) of the HB distributions, is about 0.1 larger than the one obtained from the consideration of an "evolutionary mean" (EML) over the RR Lyrae variables at each given metallicity, alpha(EML), being moreover different from the ZAHB slope alpha(ZAHB). Therefore, if we take alpha(EML) congruent-to 0.17 - 0.19, as suggested by SHB models, a value alpha(LE) congruent-to 0.26 - 0.28 is expected. This scenario is compared with the available calibrations of the absolute magnitude of the HB, suggesting that it does play a significant role in the derived slopes of the several calibrations, possibly accounting for much of the existing discrepancies. A detailed comparison with new, extensive SHB calculations is also performed. Finally, it is shown that, in case our suggestion is correct, the age difference between the most metal-poor and the most metal-rich Galactic globular clusters of the halo is, in the mean, probably not significantly greater than approximately 1 - 2 Gyr.
