In ten years of observations, the IceCube neutrino observatory has revealed a neutrino sky in tension with previous expectations for neutrino point source emissions. Astrophysical objects associated with hadronic processes might act as production sites for neutrinos, observed as point sources at Earth. Instead, a nearly isotropic flux of astrophysical neutrinos is observed up to PeV energies, prompting a reassessment of the assumed transport and production physics. This work applies a new physical explanation for neutrino production from populations of active galactic nuclei (AGN) and starburst galaxies to three years of public IceCube point source data. Specifically, cosmic rays (CRs) produced at such sources might interact with extragalactic background light and gas along the line of sight, generating a secondary neutrino flux. This model is tested alongside a number of typical flux weighting schemes, in all cases the all-sky flux contribution being constrained to percent levels of the reported IceCube diffuse astrophysical flux.