I believe your approach with the other party's insurer is spot on. My wife's car was rear ended and the other party's insurer stepped in and said they would sort it and we would have no grief about ncds and it would not appear as an accident on our insurance. The car was repaired well and we had a nice mercedes hire car. But the bit about the insurance record was bollocks... as I found out when renewing my insurance which was loaded after the quote as my wife "had been involved in a traffic accident." I was accused of hiding the accident. I genuinely believed from the other party's insurers that it wouldn't be classed as an accident and they were clearly wrong....
I had a similar issue when our car was rear ended with my wife driving. I did report it to our insurers right away, but the other drivers's insurers, to their credit, acted quickly and our car was repaired through a Ford main dealer (the car was only six months old) and they arranged for a courtesy car to be delivered.. The sting in the tail - our insurers loaded our next premium. Despite my protestations they wouldn't budge - so I moved to another insurer who didn't load the premium (yes, I did inform them of the accident).
