Car backed into me and is now claiming I hit them

A couple of weeks ago, I was parallel parked in front of a duplex waiting for my friend to come out. I was facing the main road, and I was maybe 20 feet away from a stop sign. A driver pulls into the road I was on and then immediately flips a bitch to end up in front of me at the stop sign. They were pulled out into the road with no turn signal on but appeared to be trying to turn right back onto the road they came from. I started to inch forward because I realized my friends house was the closest to the stop sign, but I stopped when I realized the car at the stop sign started backing up. I was completely stationary and the driver was getting really close to my car. I honked to give them a warning and they still proceeded to back into my car 🤦🏻‍♀️ we got out, exchanged info, etc. I filed a claim with my insurance as well as theirs, but I just received a letter stating that THEIR insurance finds them to not be at fault and that I HIT THEM. They said “I failed to maintain a proper lookout, and impacted the stationary vehicle”. I’m going to contact my insurance tomorrow to see how we go from here. Any advice?