1) Was this police in an unmarked car?  If this was a standard (marked) police car, how could - why would - the pickup truck run thru the intersection? 'round here, anytime you see a police car, there is a heightened sense of alertness - you are extra cautious with your driving habits.  So, if this car had a police car, how did it get hit?

2) Anytime there is a dispute in an accident, I would turn it over to the insurance companies, and let them sort it out. Don't wrangle over details. That is what the insurance companies are there for.  Yeah, I know - it increases the insurance rates for all. However, as I said, that is what they are there for.

3) Quite a few years back, I witnessed a guy running a red light, and hitting a car. I saw it happen, and the guy clearly ran a red light - it was not even close. We called the police, and waited for them to come.  In the meantime, the guy that was hit went and talked the the driver who ran the red light.  He simply wanted that driver to admit that he ran a red light.  The driver at fault would admit to nothing. He had the "teaching" that you never admit to anything, and that is the perspective he took.  What I learned from that incident..... anytime there is an accident - no matter how small - call the police, let them get it on record, and then turn it over to insurance companies to sort out.