All of recorded human history is evidence that this is false. Consider the Holocaust, the Salem Witch Trials, Lysenkoism, The Great Leap Forward, Aztec human sacrifices, and so many others. Even if you just consider the relatively modern United States just look at Prohibition, the War on Drugs, Jim Crow Laws, and so many others.

I am against censorship, but not because I believe that bad ideas can't take hold and cause enormous damage. I just believe that the benefits of living in a society with free speech outweigh the costs.