When my Civic Type-R was resprayed for the edge of the door being buckled and scrapped similar to this scenario Honda told me they would only take the paint back halfway along the adjoining panels to the door panel they were to respray and remove the dent from. I am surprised they have to do the whole side of the car. I also don't remember the cost being as much as £700+.
I would have it done properly and go to VW if at all possible. Also if you have her details, you have to surely get the woman to pay for the damage.