Again, unlike you, I have more faith in the Family than the State and unless the child can prove that her life is in immediate danger, the State has no right to take a child from her family.
That statement is either criminally naive, or ... never mind I'll stick with criminally naive.
You keep creating false arguments. First concerning the state "having a right", which was never an issue, and now this assertion that I don't "trust the family". I acknowledge that there are some parents that abuse and kill their children. Further, I know that allowing such a thing is in itself evil.
You go further and put the burden of proof on the child. I assume that you will also defend the parents right to deny the child access to contact authorities, so you are de facto stating that a child should never be protected from harm. It is unclear if you would arrest the parents for killing a child. I assume you would, but your argument that children are not afforded any protection wouldn't support that inference on my part.
You make the colossal mistake that many Libertarians make, i.e. they cannot make any decision that isn't totally formulaic, thus they are willing to tolerate any amount of evil in fear of treading on a slippery slope.
In the real world, Due Process is a gray area of subjectivity and almost always a slippery slope, where somewhere between a harsh word and a broken arm, the legal system must decide what constitutes abuse. To put the burden of proof on a child is only slightly upstream from requiring people who are in a coma to firmly state that they want to continue getting fed.
Anyone with a smidgen of the facts understands that this girl's life is in danger. You mistakenly think that sacrificing her life will somehow set a precedent that will prevent Statists from pushing to take away YOUR parental rights. You are wrong. They have never been and are not now constrained by anything. In fact, if this girl is sent back to her parents and murdered, it will only give the statists more reason to take away rights. More restrictive laws are almost always the result of people being unwilling to logically and responsibly enforce common sense laws.
How is the state "taking" her, if it is her desire to be separated from her family? "Taking" would mean countermanding both her and her family's desires.