The skeptical mindset nowadays prevalent in the scientific community is characterized by being extremely harsh on people making false positive (type 1) errors combined with extreme leniency on people making false negative (type 2) errors.
I don't want to get into the rest of the debate, but the above is an extremely good point.
Anyone remember what happened to some of the senior people at OPERA a few years ago? (The case of the anomalous arrival times of neutrinos.) They published the anomalous results to attract possible explanations (I read their conclusion very carefully and it was pretty neutral in tone). When an explanation did appear they were roasted for publishing.
So anyone publishing a hypothetical "big result" in this case will be in serious trouble if there is any mistake...