For what it's worth (as I'm not sure it still works like this), some years ago a neighbour drove into my car. I first tried to settle amicably with no insurance companies involved. No such luck. I was concerned about loss of no claims bonus if I went through my own insurance, so I got his details from the insurance disc and went directly to them. It took a while, but they eventually paid off (didn't have to go as far as getting soilicitors involved), and they paid in full.
My inclination would be to do the same again if the liability is clear. I seem to recall cases happening in the UK where people's own insurance paid out rather than pursue the claim with the other party, with consequential loss of NCD. I could be wrong on this one though.