We describe a consequence of the Eddington bias which occurs when a single astrophysical neutrino event is used to infer the neutrino flux of the source. A trial factor is introduced by the potentially large number of similar sources that remain undetected; if this factor is not accounted for the luminosity of the observed source can be overestimated by several orders of magnitude. Based on the resulting unrealistically high neutrino fluxes, associations between high-energy neutrinos and potential counterparts or emission scenarios were rejected in the past. Correcting for the bias might justify a reevaluation of these cases.
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