I don't think the bible actually indicates that this rule applies to sexual abuse. If I remember correctly, it was more for cases of fraud. There is a rule in the bible (which has it's own problems) that if a woman is raped and no one is around, the man who raped her has to take her as his wife. This indicates that her word that the man raped her would be sufficient in this case.
Honestly, though, there are so many other problems with the bible that don't rely upon subjective interpretation to see. There are a hundred reasons that show it's not the word of god before you get to the (mis)handling of child abuse cases as a result of (mis)interpretation of certain vague scriptural rules.