Parents trying to reclaim "runaway" 19 year old.

My cousin is 19 years old and resides in Kentucky (attending a university there). She has recently been seeing counseling at the university regarding her home life and some issues with depression, and on the advice of her counselor she has come to Virginia to spend the winter break with my family instead of going home.

Her father called and claimed that if we did not send her home immediately he would call the Kentucky State Police and have her forcibly reclaimed, and that we would be guilty of "aiding and abetting" and some variation of "endangering the welfare of a child", on the grounds that she is mentally unstable for having sought counseling at school.

The obvious problems I see with his claim are:
1) She is 19
2) She has flown to stay with us of her own accord and on the advice of the counselor she has been seeing for weeks, so clearly she's not "unstable".

Does this threat have any legal grounds whatsoever? Or is it just a threat?

He has no grounds once she is of adult age, as it would seem she is now.