In the end, there's going to be fallout one way or another. It's a serious decision that's going to affect her life in a non-trivial way. If the kid is so afraid to tell her parents, and thinks there is a legitimate reason why she can't, then there should be processes in place to help her get through it and come to a decision that works best for her.
There is no perfect outcome. What we can do is try to do what's best for the girl. I think having her seek out professional help, and then going by the recommendation of that help is the best option out of list of really bad choices.