Sometimes it is better for the company or other party to come after you with a little information (not for a little information) over and over. Instead of loading them up with your own information to second guess with and prevent more calls to you.
After their second or third letter you can even ask them to send you their accident report as typically filed with the city. Then you can rebut it piece by piece. I guess here you would have to give them corrected information for each incorrect piece of their information such as "we were in Alexandria, not Roanoke that day" in the Virginia case above.
I would even do such things as have the investigator come over to see me instead of my bringing stuff in to him. As inspired by a Bruce Williams, talk show host currently residing in Florida and a Disney fan.
Now there is such a thing as and a term for it: "Non contact hit and run". Someone swerves to avoid you and he gets into an accident. This is where
being able to match up information (that they volunteer first as I suggested) can be useful.