That might be true for some people but not everyone. Do you take into account situation where someone can get treatment and change ones mind? Since you, a non-medical professional, cannot make that judgment it's better to use as a rule to always call.
Emergency visits are not about locking someone away but about figuring out a best treatment. Whether a person will follow the treatment or not that's a different story but at least someone was there for them, to listen, to help, and with means and experience to do it.