Actually it is the legislatures conclusion. The legislature has seen fit to criminalize sexual relations with a person under the age of 16. Presumably they passed that law because they see sexual relations at that age as harmful to those under 16.
Thus, any evidence of sexual relations in that group of folks requires reporting. The reasonable would seem to only come in to play when deciding whether or not sexual realtions indeed happened. Pregnancy (read abortion), the root of the opinion and the court case would seem to be pretty solid evidence that sexual relations had happened. Since sexual relations under the age of 16 is criminal, the reporting of those relations is madatory.
The Attorney General's opinion is just that and the Tenth Circuit has already found his basis rational and overturned this Judges injunction.
However, the person under 16 isn't the person committing the crime. The law makes it a crime to have sex with an underage person, but the law doesn't punish the minor. The law punishes the adult. That's the big blunder in the 10th Circuit's opinion. The court concluded that minors have a right to informational privacy, but--since criminal activity is not protected by the right to privacy--minors don't have a right to privacy in their illegal sexual activity. This reasoning makes no sense unless you assume that the pregnant minor is the perpetrator rather than the victim of the supposed crime, which isn't at all how the law is either written or intended to be understood.
Anyway, according to the court, the district court didn't properly address other important preliminary injunction factors such as irreparable harm and balance of injuries. So it sounds to me like the injunction was rightly thrown out, but that's no indication of how the case will ultimately turn out. I expect the state will lose.