Overconfidence doesn't change the probabilities of the rare, harmful events that they are predicting won't happen. But their bias against self-doubt does increase their willingness to bet against unprecedented events.. n=1001 safe observations (where E[payoff] > 0) cannot predict that the next will be catastrophic (E[payoff] = -inf, or at least absolute value >> O(N*E[payoff seen up till then])) with non-zero probability beforehand; the expected payoff would appear vastly different before the event than after. The bets they choose will reflect the way they underestimate the consequences of speculation.
Evidence of absence > absence of evidence, another way to put that is the weight of ¬valid(test) >> the weight of ¬¬valid(test), so we should not decide the test is invalid just because it's not yet invalidated.
My gut feeling is that the upper-bound of proven benefit (to individuals/society) of the test (even if ~99.99% accurate) << upper-bound of the harm (intentionally or not) - because 'invalidity' isn't a question of whether a test is always non-satisfiable, the burden of proof falls upon the one introducing it, rather than the one rejecting it.
The potential for ostracism is just too great.