I'm guessing the sun is easily ruled out based on the direction the neutrino was travelling (as measured by the momentum of the particle produced when the neutr

I'm guessing the sun is easily ruled out based on the direction the neutrino was travelling (as measured by the momentum of the particle produced when the neutrino interacts with something). "Random galactic neutrinos" are probably a statistical exclusion: Although there could be a tau neutrino coming from the same direction as the experimental neutrino source, there aren't enough of them to create any significant chance of the observation being anything other than an experimental neutrino.