Kids are always a result of their parents. Fuck all you shitty Moms out there.
No they can't make you enter the hospital. But they can and sometimes do work things out with the doctors in order to lock you in. With lies of your use or behaviour.
The best way to avoid it all is to just maintain positivity and always turn the other cheek. Never freak out or overshow emotion, or they'll just selectively interpret something you say and bring in the cart. Crazy parents can do crazy things to make you seem crazier than they.
Oh and dude if they do get her tell her that she can request that her parents not be allowed to speak to the doctors at the hospital. Tell her to cut off her other doc too. Then the place will keep her there the minimal amount of time and when the time comes for them to decide what to do with her, if she's behaved normally and has normal health she should be able to leave with you or a friend. They really won't keep you there if you remove their ability to contact the people you are with on the outside, then they can't get any information on you, you don't freak out and give any to them, and then you calmly and rationally show that you are fine and book the fuck out.