Cash pay-out

I'll try to make this as short as possible. I'm the victim of a parking lot rear end accident. The guy who hit me has admitted all liability. I've gotten an estimate at a shop of my choosing. His insurance company (AAA) sent out to my house an independent appraiser. She did her report but failed to include pictures of the most expensive damage (There's a difference of $500.00 comparing her report and the body shop that I took my car to). After I received the appraisers estimate I called AAA and they said that if I wanted a cash pay-out I would be the one responsible for getting the proof that the part the appraiser 'conveniently' left out was really damaged. This would be at MY expense. AAA, says that my bumper has to be completely dismantled to prove this. I say, BULL!!! U see, the problem is, it's my car that got hit. If the other party has admitted all liability I shouldn't have to pay a dime, not to mention that it's none of AAA's business if I get the car fixed or not. Am I right? BTW, Totaling the car out is not an option seeing as though it's worth much more than the damage caused. This is not in dispute. I live in California. Thanx in advance.