  We demonstrate by numerical flux calculations that neutrino beams producing
the observed highest energy cosmic rays by weak interactions with the relic
neutrino background require a non-uniform distribution of sources. Such sources
have to accelerate protons at least up to 10^{23} eV, have to be opaque to
their primary protons, and should emit the secondary photons unavoidably
produced together with the neutrinos only in the sub-MeV region to avoid
conflict with the diffuse gamma-ray background measured by the EGRET
experiment. Even if such a source class exists, the resulting large
uncertainties in the parameters involved in this scenario does currently not
allow to extract any meaningful information on absolute neutrino masses.
