I agree with you that the insurance company wants to minimize their loss.
And I believe that the video along with your explanation
potentially could help you argue that you were not partially at fault for the accident.
However, the video could also work against you. I would leave
out of any explanation that you were concentrating on the light in your lane and the traffic in the oncoming lane and could not pay attention to the other cars around you. It is your job as a driver to be aware of
everything that is going on around you, even the drivers who are driving irresponsibly next to you.
Keep in mind that this is just my opinion after viewing the dash cam video. Take it for what it’s worth, an opinion offered by some guy on an internet forum.