Context. A fundamental subject in extragalactic astronomy concerns the formation and evolution of late-type galaxies (LTGs). The standard scenario envisages a two-phase build-up for these systems, comprising the early assembly of the bulge followed by disk accretion. However, recent observational evidence points to a joint formation and perpetual coevolution of these structural components. Our current knowledge on the properties of the bulge and the disk is, to a large degree, founded on photometric decomposition studies, which sensitively depend on the adopted methodology and enclosed assumptions on the structure of LTGs. A critical assumption whose validity had never been questioned before is that galactic disks conserve their exponential nature up to the galactic center. This, although seemingly plausible, implies that bulge and disk coexist without significant dynamical interaction and mass exchange over nearly the entire Hubble time. Aims. Our goal is to examine the validity of the standard assumption that galactic disks preserve their exponential intensity profile inside the bulge radius (RB) all the way to the galactic center, as is generally assumed in photometric decomposition studies. Methods. We developed a spectrophotometric bulge-disk decomposition technique that provides an estimation for the net (i.e., disk-subtracted) spectrum of the bulge. Starting from an integral field spectroscopy (IFS) data cube, this tool computes the integrated spectrum of the bulge and the disk, scales the latter considering the light fraction estimated from photometric decomposition techniques, and subtract it from the former, thereby allowing for the extraction of the net-bulge spectrum. Considering that the latter depends on the underlying assumption for the disk luminosity profile, checking its physical plausibility (for instance, positiveness and spectral slope) places indirect constraints on the validity of the disk’s assumed profile inside the radius R⋆ < RB. In this pilot study, we tested the following three different disk configurations: the standard exponential disk profile as well as a centrally flattened or down-bending exponential disk profile. Results. A systematic application of our spectrophotometric bulge-disk decomposition tool to a representative sample of 135 local LTGs from the CALIFA survey yields a significant fraction (up to ∼30 (20)%) of unphysical net-bulge spectra when a purely exponential (centrally flattened) intensity profile is assumed for the disk. This never occurs for disks’ profiles involving a centrally decreasing intensity. Conclusions. The obtained results suggest that, for a significant fraction of LTGs, the disk component shows a down-bending beneath the bulge. If proven to be true, this result will call for a substantial revision of structural decomposition studies for LTGs and it will have far-reaching implications in our understanding of the photometric properties of their bulges. Given its major relevance, it appears worthwhile to explore the central stellar surface density of galactic disks further, through an improved version of the spectrophotometric decomposition tool presented here and its application combining deep surface photometry, spatially resolved spectral synthesis, and kinematical analyses.