Unfortunately the police's assignment of fault isn't always what the insurance companies go off of, because criminal fault and civil liability are different standards.
It's easy for Officer Barbrady to say "Well she was in your lane, she gets the fine, you don't". But the insurance company then will want to know why she was in your lane. Did you have your high beams on and she couldn't see the line? Was there something wrong with the road? Was her car out of alignment? These are the kinds of games they play.
My mothers neighbor backed into her a few years ago and the cop wrote the accident report saying both parties were at fault and they had backed into each other. If the insurance went by that she would be screwed. But police are not witnesses and make crap up. My mom's lincoln had one of them fancy pants black boxes that said when, where, and how the accident happened. Most importantly that she was in drive and moving forward when she was hit. The insurance company used that info and disregarded the police report.
Same thing when the tree fell on my car, the cop wrote it up as me running into a fallen tree. But the insurance company was smart enough to ask, " how did your roof get smashed hitting a tree head on? " and got another witness statement. So they threw out that police report as well.
I know its frustrating with such a dumb cut and dry accident like this, just giving examples of why that police report is meaningless to the insurance company and they want real statements. Pretty much any info the insurance company can gather is better than a sloppy hand written note by a guy who wasn't even there, aka a "police report".