Aims. Filtergrams obtained in Ca II H, Ca II K, and Hα are often employed as diagnostics of the solar chromosphere. The vastly disparate appearance between the typical filtergrams in these different lines calls into question the nature of what is actually being observed. We investigate the lack of obvious structures of magnetic origin such as fibrils and mottles in on-disk Ca II H and K images. Methods. We directly compare a temporal sequence of classical Ca II K filtergrams with a co-spatial and co-temporal sequence of spectrally resolved Ca II 854.2 images obtained with the Interferometric Bidimensional Spectrometer (IBIS), considering the effect of both the spectral and spatial smearing. We analyze the temporal behavior of the two series by means of Fourier analysis.Results. The lack of fine magnetic structuring in Ca II K filtergrams, even with the narrowest available filters, is due to observational effects, primarily contributions from the bright, photospheric wings of the line that swamp the small and dark chromospheric structures. Signatures of fibrils remain, however, in the temporal evolution of the filtergrams, in particular with the evidence of magnetic shadows around the network elements. The Ca II K filtergrams do not appear, however, to properly reflect the high-frequency behavior of the chromosphere. Using the same analysis, we find no significant chromospheric signature in the Hinode/SOT Ca II H quiet-Sun filtergrams.Conclusions. The picture provided by Hα and Ca II 854.2, which show significant portions of the chromosphere dominated by magnetic structuring, appears to reflect the true and essential nature of the solar chromosphere. Data that do not resolve this aspect, whether spatially or spectrally, may misrepresent the behavior the chromosphere.