I believe you can in fact be committed, but not for very long. But a responsible adult would know there is something wrong or they're having a bad spell and would go for help. There are suicide hotlines, BPD forums, specialized therapists. You can go to the emergency room and they can coordinate with your mental health team. You can be given medication that will work quickly. But JA did none of this. I don't think her parents did either, even though Matt told them to. If her parents had called a hotline, they would have been helped with a plan of action.
People can't help it if they're born with a wonky brain or their brain chemistry goes on the fritz, but they can be taught to recognize when it's an issue and how to address it. The exceptions to this, I suppose, would be in the category of non compos mentis (e.g. with dementia), or physically ill (e.g. from cancer in the brain), developmentally impaired, or generally not able to distinguish right from wrong because of an organic issue (e.g. schizophrenia).
Jodi was responsible for getting help. She didn't. She actively resisted it.