How do I know that average people do not believe the one in five women raped on campus meme? Because parents still are sending their daughters to college, that's why. In increasing numbers that threaten to overwhelm males on campus. What is more, I sat recently through new parent orientations at a famous college and parents asked zillions of stupid, trivial questions and not one of them inquired into the safety of their daughters on campus or the protections afforded them. Everyone knows that some women are raped and badly taken advantage of on campus, but everyone also knows the one in five number is overblown BS.
Imagine that there is a country with a one in 20 chance of an American woman visiting getting raped. How many parents would yank their daughters from any school trip headed for that country -- a lot of them, I would imagine. If there were a one in five chance? No one would allow their little girls to go. I promise. I am a dad, I know.
Even if the average person can't articulate their source of skepticism, most people understand in their gut that we live in a post-modern world when it comes to media "data". Political discourse, and much of the media, is ruled by the "fake but accurate" fact. That is, the number everyone knows has no valid source or basis in fact or that everyone knows fails every smell test, but they use anyway because it is in a good cause. They will say, "well one in five is probably high but it's an important issue anyway".
The first time I ever encountered this effect was on an NPR radio show years ago. The hosts were discussing a well-accepted media statistic at the time that there were a million homeless people (these homeless people only seem to exist, at least in the media, during Republican presidencies so I suppose this dates all the way back to the Reagan or Bush years). Someone actually tracked down this million person stat and traced it back to a leading homeless advocate, who admitted he just made it up for an interview, and was kind of amazed everyone just accepted it. But the interesting part was a discussion with several people in the media who still used the statistic even after they knew it to be outsourced BS, made up out of thin air. Their logic: homelessness was a critical issue and the stat may be wrong, but it was OK to essentially lie (they did not use the word "lie") about the facts in a good cause. The statistic was fake, but accurately reflected a real problem. Later, the actual phrase "fake but accurate" would be coined in association with the George W. Bush faked air force national guard papers. Opponents of Bush argued after the forgery became clear to everyone but Dan Rather that the letters may have been fake but they accurately reflected character flaws in the President.
And for those on the Left who want to get bent out of shape that this is just aimed at them, militarists love these post-modern non-facts to stir up fear in the war on terror, the war on crime, the war on drugs, and the war on just about everyone in the middle east.
PS- Neil deGrasse Tyson has been criticized of late for the same failing, the use of fake quotes that supposedly accurately reflect the mind of the quoted person. It is one thing for politicians to play this game. It is worse for scientists. It is the absolute worst for a scientist to play this anti-science game in the name of defending science.