There is this pervasive and widespread inability to even conceive of suicide. For most, it's not fathomable or reasonable under any circumstances. It just cannot be grasped by the population at large - it's always something preventable, something done on impulse by people who are hurting and not thinking clearly. I resent that mentality, but I have accepted it as a given when dealing with those who don't know what it's like to think about ctb on a regular basis.
In this instance, it is very clear that this girl was determined to end her life, irrespective of what anyone else on here said or did. She was failed by doctors and mental health professionals, not by randoms on a forum who just so happen to feel similarly to her. We all know first-hand how useless and tired the established treatment systems are. So what are we going to do? Say "get help" when the article even acknowledges she couldn't get any? Force her back to the same old tired institutions that don't know how to treat people? It's a no-win situation until we start establishing better (and low threshold) resources for people in pain.
Nonetheless, I do feel terrible for the family and this is why I personally avoid giving advice when it comes to methods. It's just not my place to offer that information up. You want the details, you look it up yourself.