You are absolutely right. For deviations beyond, say 4 or 5 sigma, it's much more probable that it's not a statistical fluke, but a systematic error. Assumption

You are absolutely right. For deviations beyond, say 4 or 5 sigma, it's much more probable that it's not a statistical fluke, but a systematic error. Assumption wrong, experiment wrong, theory wrong or something like that. We expect that measurements land within +-1 sigma of the true value with ~68% probability (and 95% for +-2sigma). Implicitly, we assume a Gaussian distribution (often the case to good approximation, at least for small deviations), and also that we can invert the sentence: the true value is within the error band around the measurement with that probability.