Its not really if it holds up in court as much as a local TV company getting ahold of the video and then showing up to the bodyshop with the van and boom mics asking questions and giving the bodyshop a terrible name.
100% talk to the shop OWNER. Not the manager. News stations would love this kind of story. I would demand a new set of tires and some sort of flat wear and tear fee.
Nice car, but you parking with your front tires touching a curb is something you definitely will want to avoid. Glad you are enjoy the MT so much more... life lesson that unless your body physically can not do it, you are never too old for a Manual.