In this case, did the state have laws on the books to prosecute such a case appropriately? I would guess no, and the best that could happen would be a prosecution for slander or something, probably max penalties of probation, not even a felony.
Other commenters have addressed the specific type cases you mention. Those cases are rare.
More common and related are they types of closely related cases I decided to address. Depending upon who is prosecuting, what state, and how the law is written, I could reasonably see women who were raped but unable to prove beyond the threshold of guilt being prosecuted for being a false accuser. I think we can agree we don’t want that to happen