Tawana Brawley is not the last person (I'm guessing) to make a false rape allegation in this world.
You seem to imply that you have worked in law enforcement. Then what I'm about to say probably makes sense.
Let's say that a policeman is confronted with a scenario in which Jane Doe accuses John Doe of rape. My intuition says that the policeman is going to err on the side of safety, that is he is not going to risk his hide even if it sounds like a bunch of baloney. He's not going to want to be the target of some politically correct witchhunt; he's going to arrest the guy even if her story sounds like something out of the Wizard of Oz. Does that make sense?