The multi-messenger era is now well underway, with high-energy neutrinos providing a unique opportunity to study particle acceleration. Recent reports describe possible coincident detections of single IceCube neutrinos with both a flaring blazar and a tidal disruption event. While compelling, these sources cannot be considered in isolation. We present various strategies to put these associations into the context of the relevant astrophysical source populations. Firstly, we can use the non-observation of point sources in IceCube searches to place constraints on the high-level properties of the unknown source population. In particular, current measurements disfavour populations of rare and bright sources. Secondly, multi-messenger simulations of proposed populations and their transient behaviour can be used to evaluate the probability of chance coincident detections in a principled manner. Finally, these simulations can also be harnessed to predict the contribution to the overall neutrino flux that is consistent with an assumed source–neutrino association. We demonstrate the application of these methods, using the proposed blazar–neutrino connection as a case study. The results raise further questions for the bigger picture of neutrino astrophysics.