Jail her too?
When my daughter was that age, the one thing that'd make her want to be with a boy I didn't like was to say I didn't like him. That's how most teenagers are (which is why I seriously contemplated suspended animation from 13 to 18 for her).
And I wouldn't use the court system to substitute for parenting, which is what the parents of this girl are doing.
I think many states have consent laws, and most are at the age of 16. What that means is although a 16 year old might get in trouble for breaking their parents rules, it is not agianst the law for an adult to have a relationship with a girl over 16 in many states.
In this case however, having a daughter myself, I side with the girls parents. If you read the story, they didn't mind the relationship except after they discovered the little sh*t was lying to them. If it had been me, I would have shown the kid my .45 ACP and explained that my daughters virtue is directly tied to the business end of the barrel. I might even let the relationship continue, with an increased amount of supervision.
I really don't like the attitude of the mother though. Sounds like she didn't care that her son was a lier and was dating a girl who was a minor and could have gotten her son put in jail for the very reason he is there. The boy is lucky there hasn't been any alegations of statutory rape. He could be tried as an adult in that case and receive a much harsher sentence than 6 months in jail.
Regardless of the will of either of the children. The boy should have been told by his mother to honor the wishes of the girls parents. Or, the boy should have had the sense not to lie in the first place. I think if he had been honest, the parents of the girl may have been uneasy about the relationship, but they probably would have allowd it. Of course that is only an assumption.