I can't see the damage so it's hard to say if I'd accept a repair and not a replacement. looks sort of like the plastic chin part that you have circled.. I can't tell. one thing I might say and the fella before me might have said it already, if the dealer saw this before you did and repaired it you probably would have never known.
I would have asked for the repair/replace to be done and if that met my approval only then would I have accepted delivery of the car. repaired to my satisfaction and a written guarantee saying the repair was covered with the 3/36000yr bumper to bumper and I'd have been good with whatever ($300) or whatever they offered.
I'd feel lucky to find the car I wanted (Grabber Blue GT Premium with glass roof, sec and comfort packages).. and haven't found one so having the car in front of me I wanted and refusing it because of a very small repair or replacement on the chin or lower bumper seems hard to understand, especially since they offered to make it right.
my 2c's, I'm picky and I'll tell you good chance this could have happened to you the first time you pulled up to park and hit a curb as it has to many Mustang owners.. if you want that car, make them fix it and if it looks good jump on it. nothing say's there's not a lot that were repaired in some way before they left the factory...
if you can't stand the idea of a repair and can't find the car you want on the lot, order a 2014 ... of course the lack of initial rebates in the early going would have more than paid for the repairs on this one, that right now wouldn't be coming out of your pocket.
just my thoughts, good luck on the decision
2011 V6 Premium ,Grabber Blue/White Stripes/Charcoal Black, Auto/2.73, 202A Pony Package, Comfort Package.
Mods, Factory Engine Cover, Ford Strut Tower Brace, 19" Painted Aluminum Wheels/245-45-19 P-Zeros, Wheel Locks, Ford Accessory Alarm, Ford All-Weather Mats, window tint, spare tire/jack, cam cap mod.
on deck... Polk Audio db571 X 4 speakers & baffles