False claims are thing thing, just not a very common thing. Most studies put the percentage of flase claims soemwhere between 2-9% of all sexual ssault accusations.
I cited a similar statistic above, that found that 6% of allegations were *proven* false. Another roughly 45% had insufficient evidence to proceed, though. What percentage of those were false, but couldn't be proven so?
Take Anita Hill. She was caught in numerous false statements, and at the time of Thomas' confirmation hearing polls showed that over 60% of Americans thought she was lying. (That number has shifted over time, to the point where the majority of Americans think she was telling the truth now.)
Is hers a false accusation? I don't think it would meet the category of that; there's no definitive proof that it didn't happen. It's just that there wasn't enough evidence and/or questions of credibility.
But, just because her allegation wasn't proven to be false doesn't mean that it is in fact accurate.
We arent taking about a small study, or even a few small studies. We are talking reviews of literally thousands of cases involving extensive police investigation. The 2-10 percentage point claim has been consistently reinforced time and time again in these studies. You can parse it however you wnat, the bottom line is that the rate of people lying about sexual assault is extremely low.
And you point out that 45% of cases go unresolved, but there is absolutely no reason to think that the rate of false reporting is substantally higher in unsolved cases than in solved cases. The police in theory investigated those case as well and could find no reason to list them as false reports. An investigation could fail to proceed for a number of reasons including the victim themslves being unwilling to proceed. Or the fact that foor the past thirty plus years people have been extremely quick to completely dismiss the victim because alcohol was involved, or her story wasn't perfect, or the man she was accusing was powerful, ect.
And then theres the fact that not all false allegations are created equal. Most false allegations are made against strangers, or fail to name a perpetrator at all (ex: I was raped by "someone,"), they typically arent hit jobs used to smear a person's character. And reporting of false allegations has so many probably including but not limited too how police themslves want to code a crime. For example if a women reports she blacked out at a party and gets a rape kit but if found to have not been assaulted police may term that "no crime," and such cases have typically led to an increased perception that false reports are a huge problem.
And when you consider the fact that most sexual assaults are never rrported you get to the heart of the issue, for one reaosn or another (shame, fear, trauma) women typically do not wnat to be identified as having been assaulted, and for that reason alone the rate of false reprorting wouldn't be expected to be that high.
Here's a good overview of the issue, if interested. http://www.nsvrc.org/sites/default/files/Publications_NSVRC_Overview_False-Reporting.pdf