If you have full coverage you shouldn't even be involved other than driving it down to the body shop. Your insurance company has to deal with getting the money out of their company not you.
Car is in the shop. Body is off and repairs started. Insurance company [other guy's] agreed that entire body need to be repainted. It ends up that after getting a better look at the extent of damage with body off car the repair estimate did increase. There was hidden damage that could not be seen with body on the car. New estimate not that far off from the $7K estimate I got from Old Dog Hot Rods in St. Louis. Now a days, when a big city shop does all the body prep, base and clear coat with cut and buff we are talking in the $10K range. That was range of quotes I got a few years ago. Blew me away then and still does.