The rate of false accusations of rape is really hard to determine but is generally regarded as being pretty low (Vicpol puts it at ~5% based on studies). It’s also extremely hard to get a good number though, since false does not mean unfounded.
I don’t think it’s justified drawing an equivalence between rape and rape accusations given the evidence we have on the rates, it makes it seem like false accusations are happening way more than they actually are.
Also given who this probably is, this is likely not the only accusation of rape also, which decreases the likelihood the accusations are false I would suggest.