I wonder if it could be a background source that we don't understand. Maybe some freak coincidence where particles come in in exactly the right angles to fake a

I wonder if it could be a background source that we don't understand. Maybe some freak coincidence where particles come in in exactly the right angles to fake a hyperenergetic photon. Or somebody messing with laser pointers. Or birds or whatever. I used to work in particle physics, and never shared the confidence of my colleagues in rare events. If you just have 3-4 signal events, considering the expected number of events, you might statistically have a discovery. But you can't be sure how your detector is going to behave for those extreme events, because you have no benchmark. You have to assume a proton is a proton, an electron is an electron, and no weird things happen at high/low energies and angles (or that you understand how things change). It is even worse if you are trying to disprove some specific model. You see no events of a certain kind. Does that mean you disproved the model, or that your setup (detector, triggers, event selection ...) is just blind in this very narrow part of the parameter space?