New South Wales seems to have specific legislation addressing situations where parents refuse to consent to procedures necessary to preserve minor children’s (<=15yo) lives.
http://www5.austlii.edu.au/au/legis/nsw/consol_act/caypapa1998442/s174.html
(1) A medical practitioner may carry out medical treatment on a child or young person without the consent of–
(a) the child or young person, or
(b) a parent of the child or young person,
if the medical practitioner is of the opinion that it is necessary, as a matter of urgency, to carry out the treatment on the child or young person in order to save his or her life or to prevent serious damage to his or her health.
Note that the article from OP mentions the lawsuit was actually brought by the hospital.
The government handbook on consent has an example that gives some insight as to the law,
Sarah is a 17-year-old patient who has Hodgkin’s disease and is about to start her third round of chemotherapy following a relapse of the disease. Sarah and her family are followers of the Jehovah’s Witness faith and object to having a blood or platelet transfusion. Sarah and her parents have provided a written, signed document to her Medical Practitioner refusing blood or platelet transfusions. Sarah’s Medical Practitioner has over 20 years’ experience with patients in similar situations and has advised that Sarah will die without chemotherapy treatment. Sarah has a 70% chance of being cured of the disease with chemotherapy treatment, but this treatment will necessitate a blood transfusion, without which Sarah is likely to die from anaemia.
Sarah and her parents seek to have the chemotherapy treatment but refuse to consent to a blood or blood product transfusion. Sarah has been assessed by expert Medical Practitioners as a Mature Minor. She is fully supported by her parents in her decision.
As Sarah is a minor, her refusal of treatment may potentially be overridden by her parents or the court, notwithstanding the fact she is both intelligent and mature. However, before approaching the court, the Medical Practitioner should consider following the procedures set out in this Consent Manual and:
(a) consider any alternative appropriate treatment for which consent would be forthcoming
(b) consider obtaining a second opinion from a suitably qualified Medical Practitioner to confirm the prognosis and treatment plan
(c) attempt to reach agreement with Sarah and her family by repeat discussions and counselling
(d) if no agreement can be reached, consider whether the refusal of treatment means that there are reasonable grounds to suspect that Sarah is ‘at risk of significant harm’ to the degree that a suspected risk of significant harm report must be made to the Department of Communities and Justice pursuant to the mandatory reporting requirement under section 27, Children and Young Persons (Care and Protection) Act 1998.
Finally, the Medical Practitioner should escalate the issue within the Health Service and urgently seek advice from Ministry of Health Legal Branch to obtain an appropriate court order for guidance on a treatment plan. In this situation, the court may invoke its’ parens patriae jurisdiction to make an order based on the best interests of Sarah.
In making its decision the court is likely to take into account the nature of the disease, the nature of the treatment, the reasons for the treatment, the desirability of the treatment, the risks to Sarah’s health with and without the proposed blood transfusions, the faith and views of Sarah and her parents, and the views of the attending Medical Practitioners.
So you see even if the patient was older and more competent and had religious objections, with full support of the parents and only a 70% success rate, the court can literally decide to force the treatment in the name of the patient’s best interests.
In the present case we seem to have a higher success rate and furthermore statutory deference to the doctors, and statutory criteria of life and limb rather than quality of life.
~Max