We test the "reprocessing paradigm" of optical-UV active galactic nucleus (AGN) variability, according to which the variations in this wavelength range are driven by a variable X-ray component, by detailed modeling of the correlated X-ray-optical (3590 and 5510 Angstrom) variability of the recent multi- wavelength campaign of NGC 3516. To this end we produce model optical light curves by convolving the observed X-ray flux with the response function of an infinite, thin accretion disk, illuminated by a pointlike X-ray source located at a given height h(X) above the compact object (the lamppost model). We also produce the ionized X-ray reflection and Fe K alpha line spectra that result from the reprocessing of the same X-rays on the disk surface. Then we compare the properties of the model light curves (amplitude, morphology, lags) as well as those of the Fe K alpha line profiles to those observed. Our calculations improve on those of similar past treatments by including the effects of an X-ray-heated ionized layer in hydrostatic equilibrium on its surface, which greatly affects its X-ray timing and spectral properties. The results of our calculations do not provide a clear-cut picture that would either support or refute the reprocessing paradigm: despite the large (similar or equal to 50%) amplitude excursions of the X-ray flux, the model optical light curves exhibit variability amplitudes of only 3%-4% and vary in synchrony in the two bands, in agreement with observations. However, the model light curves, when viewed in detail, do not have a direct correspondence to those observed. Futhermore, while the observed intraband synchrony generally points toward smaller values for the black hole mass (M = 10(7) M.), the X-ray Fe K alpha line, X-ray reflection, and optical-UV spectra seem to favor larger mass values (M = 10(8) M.). Generally, no combination of the model parameters seems to produce agreement with the ensemble of the constraints imposed by optical/ UV/X-ray spectral and timing observations; we are thus led to believe that the simplest version of the lamppost model geometry is inconsistent with the NGC 3516 observations.
