I've actually heard the opposite claim made by systems researchers, and this has been extended to other empirical researchers as well. Namely, "you're as good as your worst result" (presumably thresholded to ignore grad school). The rationale here appears to be that in the conservative empirical sciences, where a badly designed experiment can cast a shadow on all your later work, it's your worst result that matters.
I can see how this works (sort of): in the more mathematical disciplines, a "proof" can to a large extent be validated independent of the author, so mistakes in past proofs can be tolerated (though if this becomes an endemic problem, then ...). Louis de Branges is famous for his proof of a conjecture in complex analysis known as the Bieberbach conjecture, and is currently well known for his claimed proof of the Riemann Hypothesis (Karl Sabbagh's book on this has more on de Branges). His proof of the Bieberbach conjecture was not without some initial skepticism from other mathematicians, because of some earlier false starts. However, it was soon seen as correct, and has opened up new areas of mathematics as well. As a consequence, his proofs of the Riemann hypothesis have received more cautious consideration as well (although I am not aware of the current status of his claims).
On the other hand, validating empirical work is largely on trust: you trust that the scientists have made faithful measurements, have kept proper lab notes etc, and I can see how a weakening of that trust can lead to much higher skepticism.
In this light, it's interesting to read Malcolm Gladwell's latest article for the New Yorker. He profiles the "profilers": the psych experts who help the FBI track down serial killers, and comes to this conclusion:
He seems to have understood only that, if you make a great number of predictions, the ones that were wrong will soon be forgotten, and the ones that turn out to be true will make you famous.