“Really?” John Humphrys pressed Alison Saunders, the director of public prosecutions, on the BBC’s Today programme when she was explaining that an acquittal doesn’t imply a woman reporting a rape has made a false or malicious allegation. Hopefully, his sceptical intonation was an interviewing technique. But it came across as an indication that he (like many others) labours under the misapprehension that if someone isn’t found guilty beyond reasonable doubt in a court of law, that’s a sign that their alleged victim was lying.

Humphrys was interviewing Saunders about the Crown Prosecution Service’s annual crime report on violence against women and girls. He chose to focus a good chunk of the interview on the issue of false allegations, which leaves the utterly misleading impression that this is the main issue in the prosecution of rape, rather than levels of under-reporting (although reporting of rape has increased in recent years, only around 15% of sexual violence is reported to the police); or the lack of specialist support for women coming forward to report rape; or the way that some women reporting rape have been met with active disbelief by the police. None of these issues surfaced in the interview. Neither did it explore why conviction and prosecution rates for domestic violence offences are declining, which was also highlighted in the CPS report.

That’s not to say there are no false and malicious allegations. But there is no evidence to suggest that they are higher for rape than for any other crime, despite the damaging perceptions to the contrary. If anything, they make up a tiny proportion of reported rape cases: a landmark study by the CPS found that in a 17-month period, while there were just under 6,000 prosecutions for rape, there were only 35 for making false allegations of rape. A significant number of these cases involved young, often vulnerable people – some with mental health issues.

Many rapes are reported that don’t meet the evidential bar for prosecution. It doesn’t mean the rape didn’t happen

Of course, one false allegation is, like any crime, one too many. But our whole justice system is geared around the possibility of false allegations. It’s why we don’t take everyone accusing someone else of a crime at their word. It’s why we impose a high evidentiary bar before someone can be convicted of a crime, asking juries to apply a “beyond reasonable doubt” test.

There is nothing like jury service to remind you of the imperfections of our justice system. I was once a member of a jury that didn’t convict someone who I thought was probably guilty of the crime of which they were charged – but not “beyond reasonable doubt”. In my view, it was absolutely the right outcome. But our system means some of those who are probably guilty end up, rightly, walking free, and innocent in the eyes of the law. That doesn’t mean that a crime wasn’t committed. It certainly doesn’t follow that the plaintiff was lying.

This high evidentiary bar can make rape more difficult to prosecute than other crimes. Often, there will be no witnesses, and the fact that sexual intercourse took place is not in question; so the question is over whether consent was given, and the only eyewitness accounts will come from the accuser and the accused. Not all rapes result in the sort of forensic evidence – such as bruising, or skin underneath the fingernails – that can indicate a lack of consent. So the conviction rates as a proportion of crimes prosecuted are lower for rape than for other crimes – but beyond that, there are many, many rapes that are reported that don’t meet the evidential bar for prosecution. It doesn’t mean the rape didn’t happen.

Given the misperceptions that false allegations of rape are rife, we cannot let the notion that an acquittal somehow implies a false allegation to go unchallenged. In many cases, rape remains more difficult to prosecute than other crimes, and the suggestion that the scales have tipped too far in favour of those reporting rape rather than those who stand falsely accused of it is ludicrous. We must accept that “beyond reasonable doubt” means there are inevitably some likely rapists who will walk free. Women who have suffered sexual violence only to see prosecutions collapse – or be told that there isn’t enough evidence to prosecute in the first place – deserve specialist support, not to be subjected to the smear that they were lying all along.

• Sonia Sodha is chief leader writer at the Observer