Can a child legally run away to his non-custodial parent?

I knew a teenager in this situation and they made life such hell on the custodial parent (consistently and purposefully ruining furniture, carpet, etc.) that the custodial parent gladly allowed them to run away to non-custodial parent. They described it to me as domestic custodial terrorism. I believe the fact is that he can run away as long as the custodial parent doesn't go running to the judge. I know when I was 14 if one of my parents told me I couldn't go live with my other parent I would have done this without a second thought!