There's those neutrino detectors which detect and fail to detect rare events, for example.

OK, so? Do they impose six-sigmas on the total result, subdivisions, or what?

Yes, and they don't seem to talk much about non problems.

Yes, because almost all clinical trials stink. Publication bias is pervasive, and the methodological problems are almost universal. When you read through, say, Cochrane meta-analyses or reviews, it's normal to find that something like 90%+ of studies had to be discarded because they lacked such basic desiderata as 'blinding' or 'randomization' or simply didn't specify important things like sample sizes or intent-to-treat. That people are willing to cite studies at all is 'talking about non problems'.