I would not worry at all if she said that she wants to be "good friends". She clearly has feelings for you, but has decided to respect her parent's decision.
I had my first "real" boyfriend when I was 14. My parents didn't like it, but they let it go. I think the reason they chose to do that was because they were much more comfortable knowing where I was and who I was with rather than being constantly worried that I was sneaking around just to see him.
I completely understand your situation, and hope that it works out for the best. But whatever you do, don't try to sneak around with the girl or let her lie to her parents about seeing you. They will find out eventually, and then they REALLY won't want her to go out with you.
One healthy alternative would be to go on group dates, as PDM suggested, or just hang out together as friends with a few of your mutual friends. That way you won't lose your close relationship with her, and when the time comes for her to be allowed to date, you will be that much closer.
