@icestorm81; Sorry to hear about your misfortune. Your experience highlights one of the reasons why I don’t like diamond cut alloys - easily damaged by inexperienced tyre fitters or poorly maintained tyre changing equipment.
I wouldn’t be agreeing to the tyre fitting place repairing the damage - I’d want to get it repaired at a wheel refurb company of my choice and then get the tyre fitting place to pick up the cost of the refurb.
The copper colour is actually a tinted lacquer rather than copper coloured paint. l’d be asking whoever you get to do the refurb to confirm they’ll be able to accurately match this copper coloured lacquer tint on the machined face of the wheel. If they can’t, then depending on how OCD you are about your car, you’re then left with getting all the wheels refinished so they all match, colour-wise, or getting a new wheel to replace the damaged one and for the tyre fitting place to agree to pick up the cost.
Good luck with getting this sorted. Please keep the forum updated on progress.