Since the hospital legally can present their side of the story and evidence to support it and have chosen not to, it is reasonable to accept the patient's account as accurate.
No one else has claimed she's incompetent. Other mmedical professionals have said she was and is. When patient signed the release, they were free to discuss the details of the case. Their refusal to do so is telling.
The facts of the case are that the hospital engaged with several judges and a police department all of whom ultimately concluded that they had no legal basis to hold her. Yet they had been doing so anyways.
As far as I can tell determining who is at fault is exactly what the legal system is for.
And people are allowed to make stupid decisions! It's not the state's responsibility to automatically defer all control to the residing 'expert'.
That is enough reason for me to consider this article to be sensasional. It is impossible to say who is at fault.
In general, it often happens that people think they know better than doctors, and in this case she may simply be lucky that she did not get seriously ill. The article itself contains a lot of incoherent quotes and it is impossible to make any sense or argument from it.