If you have gone through insurance as you suggest it will go down as a non fault accident. I have previously watched these small dent companies that come to your home, paint several area’s of a neighbours deceased fathers picanto, where they didn’t even bother to tint the paint to make it suit the aged standard red of the car. Needless to say it looked idiotic.
I wasn’t given a choice about where the car was repaired but if I had been then I probably would have chosen the mobile option anyway, as I have modifications to my vehicle and trying to get a suitable hire vehicle whilst mine was away would have been difficult. I just assumed that you would get the same quality of repair wherever the vehicle was.