Warped extra dimensions can address both the Planck-weak and flavor hierarchies of the Standard Model (SM). In this paper we discuss the SM neutrino mass generation in a scenario in which a SM singlet bulk fermion-coupled to the Higgs and the lepton doublet near the IR brane-is given a Majorana mass of order the Planck scale on the UV brane. Despite the resemblance to a type I seesaw mechanism, a careful investigation based on the mass basis for the singlet four-dimensional modes reveals a very different picture. Namely, the SM neutrino masses are generated dominantly by the exchange of the TeV-scale mass eigenstates of the singlet, that are pseudo-Dirac and have a sizable Higgs-induced mixing with the SM doublet neutrino; remarkably, in warped five-dimensional (5D) models the anticipated type I seesaw morphs into a natural realization of the so-called "inverse" seesaw. This understanding uncovers an intriguing and direct link between neutrino mass generation (and possibly leptogenesis) and TeV-scale physics. We also perform estimates using the dual conformal field theory picture of our framework, which back up our 5D calculation.