Yup, some plonker did the same to me in my last A3. I saw a dog on the footpath a good bit ahead and braked in case he tried to cross the road, the car ahead didn't see him and creamed him, sent him spinning into the other lane and he got hit again. I was stopped well back from the car in front when a dude in a berlingo hit me from behind without leaving any skidmarks so can't have braked too much. He then proceeded to tell me to feck off and drove off. I got his registration number and managed to track him down (even though the car wasn't in his name - it was in the name of the owner before the last one). I gave the details to the police, but it turns out his family were known smugglers and gangsters and the police chose not to get involved. I pretty much solved the crime for them and they did nothing!
I thought I'd need a new bumper, but my repair dude said he'd be able to sort it as there was no damage to the rear bar thing. I suppose the fact that I didn't have my foot on the brake might have helped.
Most good repair shops for that kind of damage will prefer to repair it rather than fit a new bumper as they don't like to take a risk on not getting the bumper to match the colour of the rest of the car.
I suppose it all depends on how much damage has been done to the bumper.