The IceCube experiment recently detected the first flux of high-energy neutrinos in excess of atmospheric backgrounds. We examine whether these neutrinos originate from within the same extragalactic sources as ultrahigh-energy cosmic rays. Starting from rather general assumptions about spectra and flavors, we find that producing a neutrino flux at the requisite level through pion photoproduction leads to a flux of protons well below the cosmic-ray data at ~10^18 eV, where the composition is

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... t, unless pions/muons cool before decaying. This suggests a dominant class of accelerator that allows for cosmic rays to escape without significant neutrino yields.