The general order for insurance is:
1. Repair it
2. Replace with 3rd party (if available)
3. Replace with used (swap 2 & 3 if 3 is cheaper)
4. Replace with new
They will get you back to how you were before. So if they do (1) and it doesn't look right, they'll move up to the next step until you were are you were before.
So if you're stuck, just let them repair it then point out all the flaws that you see. Waste of time, but you gotta play the game if you want to win!