Herschel/PACS observations of 29 local (ultra)luminous infrared galaxies, including both starburst and active galactic nucleus (AGN) dominated sources as diagnosed in the mid-infrared/optical, show that the equivalent width of the absorbing OH 65 μm Π_(3/2) J = 9/2-7/2 line (W_(eq)(OH65)) with lower level energy E_(low) ≈ 300 K, is anticorrelated with the [C II]158 μm line to far-infrared luminosity ratio, and correlated with the far-infrared luminosity per unit gas mass and with the 60-to-100 μm far-infrared color. While all sources are in the active L_(IR)/M_(H2) > 50L_☉/M_☉ mode as derived from previous CO line studies, the OH65 absorption shows a bimodal distribution with a discontinuity at L_(FIR)/M_(H2) ≈ 100 L_☉/M_☉. In the most buried sources, OH65 probes material partially responsible for the silicate 9.7 μm absorption. Combined with observations of the OH 71 μm Π_(1/2) J = 7/2-5/2 doublet (E_(low) ≈ 415 K), radiative transfer models characterized by the equivalent dust temperature, T_(dust), and the continuum optical depth at 100 μm, τ_(100), indicate that strong [C_(II)]158 μm deficits are associated with far-IR thick (τ_(100) ≳ 0.7, N_H ≳ 10^(24) cm^(–2)), warm (T_(dust) ≳ 60 K) structures where the OH 65 μm absorption is produced, most likely in circumnuclear disks/tori/cocoons. With their high L_(FIR)/M_(H2) ratios and columns, the presence of these structures is expected to give rise to strong [C_(II)] deficits. W_(eq)(OH65) probes the fraction of infrared luminosity arising from these compact/warm environments, which is ≳ 30%-50% in sources with high W_(eq)(OH65). Sources with high W_(eq)(OH65) have surface densities of both L_(IR) and M_(H2) higher than inferred from the half-light (CO or UV/optical) radius, tracing coherent structures that represent the most buried/active stage of (circum)nuclear starburst-AGN co-evolution
