That really should depend.
It's fucked, but there needs to be malicious intent behind it. If she was actually raped, and really did believe thus guy did it, then no, we shouldn't be sending actual rape victims to prison.
There's a difference between a false ID you believe to be true and a false ID given maliciously.
I got a $100 fine because the curtains I decorated my bedroom with were visible to the outside and not an approved color.
Never again.