Vehicle Insurance doesn't want to pay?

Several weeks ago I was driving through a parking lot and a lady backed into my car. She did not start backing out until I was almost even with her so she ended up hitting my back passenger door as I was driving by. In the city this happened in, the police will not come by and make a police report if it is on private property (which it was in a supermarket parking lot) and there were no witnesses so basically it has been my word against hers. I have had my car inspected by my insurance company & also hers. I do not want to pay my $500 deductible to get my car fixed all because this lady backed into me so I feel that her insurance should have to pay for it. I received a letter in the mail from her insurance co. saying that I was at-fault b/c of failure to yield right-of-way, improper lookout, and improper lane usage. I called them to find out why and they said this lady is telling them a different story. She is saying that she was already backed out completely and in the process of going forward when I tried to go around her. It just makes me so mad that she is lying! They said to fight it my insurance co. will have to file arbitration and IF they were to win then I would be reimbursed my $500 deduct. but I don’t have $500 to spend right now! Why can’t people just be honest?? Is there anything I can do in this situation??
Well whats bad is the lady that backed into me worked at the supermarket so I’m sure she has already looked into it but even if she hasn’t I’m not sure they would be willing to help me. I have insurance with Progressive but since the police wouldn’t come out for a police report, they act like there isn’t anything they can do it is just her word against mine. The only thing they told me may be possible is the whole arbitration thing and I’m not exactly sure what happens in that situation but from what they told me they take Allstate (the other insurance co. that the lady has) to court and a 3rd party decides who is at fault.