I had a similar rear end shunt recently. Fairly minor looking, but I imagine the bumper was hiding the full extent of the damage. The bumper was damaged as was the boot lid. The inner crush bar was bent, the plastic under tray was buckled suggesting something has moved and stayed that way. There was slight deformation of the lower right boot aperture meaning the tailgate was 'sprung' -it would open and close, but not as nicely as it should.
Anyhow when I got home THEIR insurance (Admiral) rang me (not what I was expecting at all) saying it was an open and shut case, their fault and could they handle the repair. Going through my insurance would cost everyone time and money, when they could deal with the whole thing quickly and cleanly. After mulling it over I agreed. I had to notify my insurance, but instructed them not to pursue the claim.
My car was given an initial visual repair ***essment of £2300. At that figure I
fully expected a write off. Anyhow, they agreed to repair it subject to the damage not being more extensive once the bumper was off. Had I reversed into a bollard or something, I would probably lived with the damage. The '05 is getting long in the tooth and as much as I love it, that sort of money is silly.
That was three weeks ago. Once the bumper was off the cost rose 'slightly' (I don't know by how much) which called for a new authorisation before they could proceed. Two weeks ago (much to my surprise) Admiral agreed, so as far as I know the work is under way. I'm due to get the Accord back next Friday or sooner with a fully warrantied repair. Time will tell what it looks like...
As an aside the Megane I was given as a loaner was truly awful. I've never really liked Renault, but never actually driven one. Just horrible. How it got passed the first design meeting is beyond me. And then they go and stick a load of 'features' on as though somehow that fixes the underlying poor design (I could write an extensive list). Luckily one of the rear seat belts was faulty meaning it had to go back
I'm now in a bottom of the range Hyundia I30. And you know, I rather like it. I miss the leather, the space, the climate control, the cruise, the turbo (it's a 1.2 petrol with
zero power that makes an economical 48mpg -the same as my 2.2 diesel!)
As for your case, I'd be concened that if the body shop are doing it for free they'll do as cheap a job as possible.