So first- recall my statement that it's incredibly rare
outside of severe mental illness. Secondly, we've been talking about cases where someone specific is accused. The vast majority of cases deemed to be false rape cases
don't involve an accusation against someone.
The UK did a study on this, and only 39 out of 216 false rape claims involved naming a specific person. This study is one the most comprehensive studies of false rape claims ever made. So that means that only about 18% of false rape claims involved a specific person being accused.
Based on the FBI study you cited and the UK study, that means that we're talking about a [.9% - (% of accounts from people with severe mental illness)] chance that this story is a false accusation.
So yes, false accusations against specific people are
incredibly rare