A lot of these "false claims" are going to be real claims that just failed to convince a jury/judge beyond all reasonable doubt
Absolutely not. For someone to be convicted of making a false claim it has to be proven beyond reasonable doubt that she did so. Reasonable doubt about the guilt of the alleged rapist does not get anywhere near proving beyond reasonable doubt that the allegation was false.
The authorities are hesitant about prosecuting people for making false rape claims so such prosecutions are rare. That does not, of course, guarantee that everyone convicted is actually guilty. You can never completely eliminate the possibility of miscarriages of justice. But for someone to be convicted the prosecution must convince a jury that, beyond reasonable doubt, their allegation was false.