When I worked in the domestic violence field, it was an often-quoted "fact" that violence against women increased on SuperBowl Sunday. The truth is, there never was any evidence to support this assertion. Advocates accepted it as fact without following up - and it hurt the credibility of the domestic violence movement.
I also recall a statement made by a young girl in the 2000 Nike commercial: "If you let me play sports, I will be more likely to leave a man who beats me." As much as we all wished this were true, there was no research to support this claim.
I learned back then that if you can't back up your statements with legitimate research, you better not make those statements. It's hard enough earning credibility as a speaker, especially when your topic is controversial. If you're not sure about a statistic or fact, double-check it. Don't lose credibility over something as basic as fact-checking.