Nassim Taleb, of Black Swan fame (or infamy), has elaborated on the concept and developed what he calls "a map of the limits of Statistics". His basic argument is that there is one kind of decision problem where the use of any statistical model is harmful. These would be any decision problems where the consequence of making the wrong decision could be inordinately high, and the underlying PDF is hard to know.
One example would be shorting a stock option. This kind of operation can lead to limitless (in theory, at least) loss; and the probability of such a loss is unknown. Many people in fact model the probability, but Taleb argues that the financial markets aren't old enough to allow one to be confident about any model. Just because every swan you have ever seen is white, that doesn't mean black swans are impossible or even unlikely.
So here's the question: is there such a thing as a consensus in the Statistics community about Mr. Taleb's arguments?
Maybe this should be community wiki. I don't know.