As they note, common sense says that if a girl needs her parents permission to get a nose-ring, why not to get an abortion? Reality for them, however, is summarized in various hypothetical cases, wondering who will help the girl navigate the legal system.
There really is a simple solution to the issue of parental notification. If a surgeon performed a gall-bladder operation or liposuction on a minor without parental permission and there were complications and/or a bad outcome, he would be sued for far more money than had he received the parents' permission before doing the surgery. Failure to obtain permission from an adult would probably be considered evidence in and of itself of negligence.
So, forget legislating parental consent and a complicated bureaucratic system for a girl to negotiate. Just pass legislation specifically stating that in medical malpractice lawsuits against abortion providers in cases involving a minor, failure to obtain permission from a parent is to be treated with the same prejudice that it would be for any other surgical procedure.
Furthermore, pass legislation specifying that malpractice insurance companies are not obligated to pay on malpractice cases involving minors receiving an abortion without parental consent.
Some adult has to take responsibility for the decision, and abortion advocates repeatedly tell us that this should be a decision between a woman (or girl) and her doctor. Logically, then, when a minor seeks an abortion, there is only one adult in the room, and that adult should take full responsibility.