I totally disagree with you when you state: No, I do not think your child would be more likely to lie about being molested nor is she more likely to lie than a child that does not exhibit that kind of behavior.
On the contrary, I firmly believe that when a child exhibits the behavior this child exhibits, she is clearly trying to catch the attention of others and she will be willling to do things that normally kids will not do, including lying about being molested. This child seems to have a problem of conduct disorder and I learned that children who have conduct disorder behave in defiant and disruptive ways, such as violating social rules or hurting other people and may, among several things, lie, cheat, or steal, by breaking into someone's house, shoplifting, and/or lying to obtain things that they want or to avoid consequences.
While I understand that the child needs to be evaluated, legally there is nothing a stranger like me can do to help her. On the other hand, the man that the girl accuses of molesting her is a victim of her condition and may end up in jail for 10 to 20 years because the system and people in our society, do not accept that a child like this girl will do whatever it takes to catch attention and does not have any problem to lie even when those lies ruin the life an innocent man. What do you have to say to all this?