Unfortunately this does happen. I think it's mostly when parents are afraid and/or uneducated. They think if they ignore the problems they will go away. Did they tell you why they wouldn't have her tested? It's a shame too because how much early interventing can help these kids.
I think the best hope for her is going to public school. It will be there that she will be evaluated, diagnosed and get the help she needs.
In the mean time I would continue talking to the parents. If you reallly want to help.....I would read as much as you can about autism and different ways that you(or the family) can personally help her. Try to be her speech therapists, her occupational therapists and help her find her voice. Offer to babysit her and try to give her some one on one time that would really help her. Sometimes it really takes a village to raise a child.
This board is FANTASTIC! So many people are willing to help and share stratigies. Ask away! We are all here to help each other and help our children.
Good luck. She is lucky to have a Great Aunt like you.