Nonionizing stellar continua are a potential source of photons for continuum pumping in the hydrogen Lyman transitions. In the environments where these transitions are optically thick, de-excitation occurs through higher series lines. As a result, the emitted flux in the affected lines has a fluorescent contribution in addition to the usual recombination one; in particular, Balmer emissivities are systematically enhanced above case B predictions. The effectiveness of such a mechanism in H II regions and the adequacy of photoionization models as a tool to study it are the two main focuses of this work. We find that photoionization models of H II regions illuminated by low-resolution (λ/δλ lsim 1000) population synthesis models significantly overpredict the fluorescent contribution to the Balmer lines; the bias has typical values of the order of a few hundredths of a dex, with the exact figure depending on the parameters of the specific model and the simulated aperture. Conversely, photoionization models in which the nonionizing part of the continuum is omitted or is not transferred significantly underpredict the fluorescent contribution to the Balmer lines, producing a bias of similar amplitude in the opposite direction. Realistic estimations of the actual fluorescent fraction of the Balmer intensity require photoionization models in which the relevant portion of the stellar continuum is adequately represented, that is, its resolution is high in the region of the Lyman lines. In this paper, we carry out such an estimation and discuss the variations to be expected as the simulated observational setup and the stellar population's parameters are varied. In all the cases explored, we find that fluorescent excitation provides a significant contribution to the total Balmer emissivity. We also show that differential fluorescent enhancement may produce line-of-sight differences in the Balmer decrement, mimicking interstellar extinction. Fluorescent excitation emerges from our study as a small but important mechanism for the enhancement of Balmer lines. As such, we recommend to take it into account in the abundance analysis of photoionized regions, particularly in the case of high-precision applications such as the determination of primordial helium.