I think there is some general confusion as to what is meant by ‘false rape allegation.’ There is no specific criminal offense of making a false allegation of rape; a woman who goes to the police and makes a deliberate or malicious false rape allegation may be charged with wasting police time, or perverting the course of justice; someone who spreads malicious gossip may be guilty of slander or libel.
The latter may be unpleasant, but it is not going to cause an innocent man to be arrested and his name published in the national media. The whole issue here is that large numbers of people (and large numbers of police officers) believe that large numbers of women are going to the police and making malicious false rape allegations, which causes large numbers of innocent men to be arrested and their names published in the national media.
In the above article, a false rape allegation is when a woman goes to the police and makes a false allegation of rape. There are going to be no instances of a woman going to the police and making a false allegation of rape that the police are not aware of, because the police are there at the time, and they are the ones deciding if an accusation is false or not.
You could argue for police incompetence here, but recent cases suggest that up until very very recently, the police were more interested in persecuting women (the case of the woman who was prosecuted when, under pressure from her abuser and his family, she falsely withdrew a true allegation) than catching rapists (the Sapphire unit that pressured women to drop their complaints; the individual officer who falsified statements to get out of doing any work). The numbers in the above article are going to be accurate.
There is, really, no such thing as an unreported false rape allegation. What is real is that large numbers of women (around 90%) do not report their rape, and mistrust and fear of the police plays a large part in that.
The statistic for unreported rapes comes from the British Crime Survey, which surveys a cross-section of the population anonymously. There is no motivation to lie on an anonymous survey – to claim that large numbers of women are lying on an anonymous survey in order to falsely inflate rape statistics is to resort to crackpot conspiracy theories.