First how long are you planning on keeping the car? And a fix depends on how badly damaged the piece. If its bent and creased pulling it only weakens the part. Cut and weld, you have to consider eventual rust issues and 100% through welds. A bad welder can really mess things up by burning and not getting 100% welds. Yes the can replace it but is all the work totally rust proofed - like at the factory - more than likely not so you'll have that potential issue. Imperfections get into welds and rust outward as do bad welds - they gets microcracks and moisture gets in - they swell and crack. When they say 99% - maybe visually - as original - never even by cutting and replacing.

With insurance certain states have a diminshed value clause where they pay you a percentage loss since the car is not going to fetch (theoretically) on trade or sale what a unblemished car would bring. I'm not talking salvage but diminshed value. They should fix the car 100% but its true value may be 10% less - they will pay you that difference aside from the repair cost.

Anyone that paints or does body work can spot a repaired car - with metallics it can be pretty obvious even if the paint color matches 100% - has to do with the spray patterns and the way the metallic paint "flows" relative to the rest of the panels. Light metallics are the absolute worse - darks or solids not so much.