You’re not going to find data that addresses this directly. But here are some things:
• The DOJ estimates that about 2-6% of rape/sexual assault reports are false.
Note that “false” doesn’t necessarily mean the complainant was lying; the estimate includes good-faith errors. (For example, if someone thinks they were assaulted by Person A and accuses them, but actually it was Person B, they count that as a “false” report.)
It’s impossible to know how often people lie about it privately/unofficially. However, DOJ estimates that well over 90% of actually-happened sexual assaults are never reported at all.
• There’s a commonly-cited statistic that 1 in 6 to 1 in 4 women are raped at some point.
For the record, that’s not quite accurate. IIRC, the research indicated that about 1 in 4 college-age women have been sexually assaulted by graduation. We’re talking about school-age sexual assault here, so I figure it’s germane.
• Multiple studies of self-admitted, unreported male perpetrators indicate that a small subset of them are repeat offenders. They do it over and over (12x each on average), and again, are never reported. I mention this because if you do the math, it matches up perfectly with the 1-in-4 statistic.
So. If you put it all together the statement appears to be true.
How common is sexual assault? Rough low estimate, 1 in 6 women.
How commonly is it reported? Official high estimate, less than 1 in 10 times.
How common are false reports? Official high estimate, 1 in 16 reports.
Phew. Also: bleh. You know what, I find this subject pretty upsetting/demoralizing, so I’ll have to do the whole link-search thing later.
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BTW, male victims are hugely under-represented in this data. (Ditto female perpetrators.) I’m positive they report even less often, and I’m betting their reports are even less likely to be false. Actually-false, not DOJ-"false".