The latest IceCube data suggest that the all-flavor cosmic neutrino flux may be as large as 10^{-7} GeV cm^{-2} s^{-1} sr^{-1} around 30 TeV. We show that, if sources of the TeV-PeV neutrinos are transparent to γ rays with respect to two-photon annihilation, strong tensions with the isotropic diffuse γ-ray background measured by Fermi are unavoidable, independently of the production mechanism. We further show that, if the IceCube neutrinos have a photohadronic (pγ) origin, the sources are expected to be opaque to 1-100 GeV γ rays. With these general multimessenger arguments, we find that the latest data suggest a population of cosmic-ray accelerators hidden in GeV-TeV γ rays as a neutrino origin. Searches for x-ray and MeV γ-ray counterparts are encouraged, and TeV-PeV neutrinos themselves will serve as special probes of dense source environments.