I sort of side with Mitchel on this.

A mentor of mine once told me that replication is useful, but not the most useful thing you could be doing because it's often better to do a followup experiment that rests on the premises established by the initial experiment. If the first experiment was wrong, the second experiment will end up wrong too. Science should not go even slower than it already does - just update and move on, don't obsess.

It's kind of how some of the landmark studies on priming failed to replicate, but there are so many followup studies which are explained by priming really well that it seems a bit silly to throw out the notion of priming just because of that.

Keep in mind, while you are unlikely to hit statistically significance where there is no real result, it's not statistically unlikely to have a real result that doesn't hit significance the next time you do it. Significance tests are attuned to get false negatives more often than false positives.

Emotionally though... when you get a positive result in breast cancer screening even when you're not at risk, you don't just shrug and say "probably a false positive" even though it is. Instead, you irrationally do more screenings and possibly get a needless operation. Similarly, when the experiment fails to replicate, people don't shrug and say "probably a false negative", even though that is, in fact, very likely. Instead, they start questioning the reputation of the experimenter. Understandably, this whole process is nerve wracking for the original experimenter. Which I think is where Mitchel was - admittedly clumsily - groping towards with the talk of "impugning scientific integrity".