You can ask, because no harm in asking, but it probably won't help. And before you ask them, ask your insurance company if they need it. A copy of the video is only any good if a) the whole incident was recorded and b) both vehicles can be positively identified.
If the video footage doesn't show the whole accident in the frame or if the vehicles involved aren't clearly identifiable, it's useless in court. And the insurance companies are not going to battle this out in a courtroom anyway, It costs tens of thousands just to prepare to go to trial, and they're not going to spend that kind of cash over an accident that costs less than that much to settle. It's just not worth it for them.
You should prepare yourself for a 50-50 settlement, just so you know. When the other insurance company disputes fault, it's because the other driver gave a different story of how the accident happened. In minor accidents with conflicting stories (and no witnesses or solid evidence), insurance companies just split the liability fifty-fifty and be done with it.