  In a recent paper, Waxman and Bahcall (PRD 59, 023002) claimed that the
present data on ultra-high energy cosmic rays imply a model-independent upper
bound on extragalactic neutrino fluxes of 2*10^-8 GeV cm^-2 s^-1 ster^-1,
independent of neutrino energy. Mannheim, Protheroe and Rachen
(astro-ph/9812398) have repeated this calculation and confirmed the WB-bound,
within a factor of 2, only at a very limited energy range of E_\nu \sim
10^(16-18) eV, while at other energies the neutrino flux is mainly limited by
the extragalactic gamma ray background to a level about two orders of magnitude
higher than the WB bound. In this paper we present a simple, (almost) no-math
approach to the problem, and discuss under which astrophysical assumptions the
WB-bound and the MPR-bound, respectively, apply. Then we discuss to which
respect these assumptions apply to presently discussed models of extragalactic
neutrino production. We note that, averaged over the observed luminosity
function, blazars are sufficiently opaque to ultra-high energy neutrons that
there is no conflict of the predicted neutrino fluxes with the cosmic ray data,
and that these models are rather constrained by their contributions to the
extragalactic gamma ray background. At present, no modifications are implied to
the predicted neutrino events from these models in active or planned neutrino
detectors.
