Reading the article answered my only question about this.. "Which was, Is the 12 year old's opinion being given weight?" At the surface, these are not "wacko fundimentalists" denying their child medical treatment against her will. She seems to know the gravity of her illness, what her options are, and is looking at it from a "quality of life" standpoint.
12 year olds are often given weight in deciding who to live with during divorce, whether or not to use birth control, even whether or not to have a child (should they be unfortunate enough to become pregnant. Most religions consider that age a good time to ask young people to consider re-committing to the faith as a "young adult." Her voice should be considered. Remission rates for many types of cancer are high. Hopefully, if something should happen later that she would change her mind, she could...