Have the licensed insurance adjuster specified by his insurance company work up the repair estimate. It may be very close to the number your repair guy came up with. If not, you may have to use a repair facility that is approved to accept the amount he authorized.
If that facility is not acceptable to you, and you choose to use your guy, you may have to come up with the difference.
In my experience, the option to take cash in lieu of repair is not likely, but YMMV.