A big problem here is that no one should be as certain of their position in this debate as 90 percent of people are. That's because no one knows how often rape accusations are false. The data law enforcement collects is awful and biased, the outside studies are all over the board (and generally awful), and the question is inherently hard to answer. You can get a feel for that from this Wikipedia article, and if you have access to academic databases you can look up all the studies the article references and see the shit-storm for yourself. Sorting through it all, I tend to think 5 percent is the best guess from all the studies, but I also think a certain shade of blue is the prettiest color. I wouldn't describe either position as factual.
More importantly, it is a dumb debate. This isn't a zero sum game, here. Society can protect both rape victims and people falsely accused of rape by 1. having law enforcement thoroughly investigate every rape accusation, 2. having the public keep an open mind and not rush either to punish the accused, absolve the accused, or ignore/shame accusers, 3. having prosecutors treat rape like the serious crime it is, and 4. having our legislatures not create rules of evidence to tip the scales either in the favor of conviction or acquittal.
Now there are real barriers to getting to that world, but they have nothing to do with this argument. When people don't take rape complaints seriously or slut-shame accusers, it isn't because those people are mistaken as to the ratio of false to true accusations, it's normally because they are misogynistic assholes. Just so, when people rush to equate an accusation of a crime with definite proof of guilt (and this happens in a lot more contexts than rape), it normally has less to do with statistics and more to do with them being impatient, judgmental assholes.
So yeah, the problems here are much deeper than a disagreement about this one fact, and this one fact is too unclear to be worth passionately arguing about anyways.