The drug war is a perfect example of this effect; we all know drugs have the potential to be dangerous but the facts become devalued when trusted sources overstate their case. 

Unfortunately a situation seems to have prevailed in which young people learn to disregard claims about drugs from figures in authority. Suggesting that ecstasy is hundreds of times more dangerous than it really is or that cod is 210,000 times more overfished than it is utterly undermines the arguments one is trying to make. This effect could explain why drug prevention programs such as DARE have been found in many cases to result in an increased level of drug use (Lilienfeld, 2007, Werch and Owen, 2002).