Interesting. In the two states I've been a licensed driver I believe it's law to exchange drivers licences and insurance information after a wreck.
When I drove a company vehicle for daily work the instructions were to trade DL & insurance info, get witness information, call my manager & police and not to discuss fault. So perhaps the truck company is trying to collect the info for CYA.
Offhand I recall 3 of my wrecks being rearenders, and in all three the other party thought it was my fault for stopping too suddenly. I never discussed fault and didn't have to; I just followed the above guidelines and it never got past the insurance companies. They know what will fly in court and what won't, and settling is cheaper than litigating for them.
In my first, though, the other guy wanted to avoid talking to the insurance company and offered to pay out of pocket. (This was after telling me it was my fault got no useful reaction from me.) There was no police report because at the time neither of us had cell phones and there were no witnesses still around or pay phones nearby, and he refused to wait for me to find a phone and call the police. (sidebar: after he drove off I wrote down everything about the accident I could think of while it was fresh on my mind: time, road conditions, a diagram of the accident, etc...while I was doing so the car I slammed on my brakes to avoid had circled back around and stopped to offer his info as a witness.) This story is getting too long so I'll cut it short by summarizing that he told me that he wanted to settle in cash, but after getting an estimate I couldn't get hold of him; I didn't wait more than a day or two and called his insurance company who was already aware of the wreck. I think that guy was trying to pull something, and I think my more-or-less prompt reporting prevented him from getting away with it.
Anyway, my advice based on my experience is to give them the insurance info, write down anything and everything about the accident if you haven't already, call both insurers if it hasn't been done already, and refuse to consider an off-the-books settlement. As I understand it the insurance people will settle it amongst themselves.
In my 3 rearend cases, all 3 acted like it was my fault but I never got any flak from the police or insurance company about it, and I didn't have to argue with anyone.
The only time I've heard of rearend cases gone bad is a 3-way rearend where the back car pushes the middle car into the front. And that can go bad if the middle driver leaves first and the other two conspire to say the middle driver hit the front driver first. This happened to my mother. Don't leave the scene first if this happens to you, and try hard to get witnesses.
For future reference, if there is a camera available at the time of the wreck, take several pictures including skid marks.
