Who is at fault? I was hit, but my fault by technicality???

Who is liable in this case? Both in error. She hit me, but insurance wants out on a technicality. What happened: I pulled into a side street to enter a parking lot. There were two entrances one directly on the corner and one roughly 2-3 car lengths down. I took the 2nd entrance. It turns out that it was one-way, but was not well marked. I did not know until i had entered the lot. I pulled in slowly, only as far in as, maybe 2 car lengths. I realized it was one way, so I was planning to simply back into a spot on my right. This is when the incident occurred. I was stopped and a woman in one of the parking spots to my left, backed out, without even looking, right into my drivers side door. It hit right where my door meets the body of my car (2 door honda) Her car was fine. Mine was not. It should be roughly 800-1000 in damages as it is a new car. This was my first accident. She admitted liability at the scene, but there was no witness. We exchanged info and i called my insurance right away. I took a picture and emailed it to her that night. It was private property so no police. At first her insurance said they would take care of it. Now, her insurance is saying it is entirely my fault b/c of one-way parking lot, but she hit me! I did enter the wrong way, but i was not moving and had she looked in her rear view, i was directly behind her. She would have hit me regardless of the direction i was facing at the time. What rules/laws/regulations can i cite or find to say who is at fault? Even if it says I am. I just want to know. I agree that i was indeed in error as far as traffic laws... However, as for the actual accident, it had nothing to do with what way i was going. She had a clear view of me, and a clear view of the street i came from, it was a very open parking lot, and it wouldn't have mattered what way i was heading. She simply did not look behind her and backed up.