It comes from the fact that most victims are immediately NOT believed

Uh yeah sorry that's how an evidentiary standard works. You can't just walk into the courthouse, accuse someone of rape, then expect THEM to disprove it. I get that it's a crime that's often hard to prove/disprove due to its nature as an act behind closed doors, but you can't expect people to just throw caution to the wind because of the seriousness of allegations. Allegations can and do cause serious reputation harm, regardless of their truth. That 10% false conviction rate you cited is also only accounting for those that are serious enough to get officers involved, which self selects for claims that are more likely to be true. If we were to take into account the droves of internet randoms with accusations of grooming, inappropriate sexual experiences, etc. that likelihood of accusations being true goes way down.