[Perfectlap]

I don't see how one adjuster can pursuit the interests of both parties equally. Even if for the sake of appearances they would need an adjuster appointed to each party, although this would be a wash since they have the same boss...

I'm not sure if a police report is so vital here. It doesn't matter if your car was past him or not.
The burden is always on the person pulling out of a parking spot. The fact that this much damage was done to the rear car strongly points towards a situation where the reversing car was very late on the brake or wasn't looking until he felt the impact. Hence his policy should bear all costs.