Appealing a collision’s decision

Last week a person ran a red light and crashed into our car causing some severe damage (our car is more than likely totaled). Was traveling normal rate of speed (less than 20 miles per hour) not from a stopped light.

Background: Our car does not have collision as it is an older vehicle, we have good liability coverage.

Both parties stopped, exchanged information, police showed up and created an incident, a uninterested witness provided a statement to the police officer that our flow of traffic had a green light and other party went through a red light. Other party claims they had a green along with us.

Provided this to both my insurance and the other persons insurance. Our insurance reviewed and ruled in our favor shutting down some questionable injury claims the other party made based on our statement and witness statement. They didn't even entertain a 50/50 "he said she said" after speaking with the officer who provided the witness's statement.

Since we do not have collision, it is really up to us to work with the other persons insurance to get them to be liable (vs using a subrogation process).

The other persons insurance is of course doing everything to wiggle out of the responsibility. They have provided the following:

1) Since they cannot speak to the witness, the witness statement is not a factor or part of any reasonable evidence

2) We had a duty due to some CVC (California vehicle code) to ensure the intersection was clear.

Based on tone and how the conversation went, I am getting the feeling they are going to come up with a shady reason to attempt to get out of it.

Does anyone have any prior experience or insight into appealing these decisions? Is there 3rd party arbitrations that you can request to get a clean fair evaluation, etc.

Any help appreciated.