In order to test the prevailing paradigm of horizontal-branch (HB) stellar evolution, we use the large databases of measured RR Lyrae parameters for the globular cluster M3 (NGC 5272) recently provided by Bakos et al. and Corwin & Carney. We compare the observed distribution of fundamentalized periods against the predictions of synthetic HBs. The observed distribution shows a sharp peak at P_f ~ 0.55 d, which is primarily due to the RRab variables, whereas the model predictions instead indicate that the distribution should be more uniform in P_f, with a buildup of variables with shorter periods (P_f < 0.5 d). Detailed statistical tests show, for the first time, that the observed and predicted distributions are incompatible with one another at a high significance level. We show that the sharp peak in the M3 period distribution receives a significant contribution from the Blazhko variables in the cluster. We also show that M15 (NGC 7078) and M68 (NGC 4590) show similar peaks in their P_f distributions, which in spite of being located at a similar P_f value as M3's, can be primarily ascribed to the RRc variables. Again similar to M3, a demise of RRc variables towards the blue edge of the instability strip is present in these two globulars. This is again in sharp contrast with the evolutionary scenario, which also foresees a strong buildup of RRc variables with short periods in OoII globulars. We speculate that, in OoI systems, RRab variables may get "trapped" close to the transition line between RRab and RRc pulsators as they evolve to the blue, whereas in OoII systems it is the RRc variables that may get "trapped" instead, as they evolve to the red, before changing their pulsation mode to RRab. Such a scenario is supported by the available CMDs and Bailey diagrams for M3, M15, and M68.

8 figures, 11 pages. Uses latest emulateapj.cls style file (included, 05/14/03) and apjfonts.sty (also included). The full-resolution preprint can be downloaded from http://www.astro.puc.cl/~mcatelan/. ApJ, in press