True story: I was once the meat in a three car rear-ender sandwich in my Karmann Ghia. When I bought the car I declared the value on the transfer papers at $1200.00. I had actually paid $3600. When the car got hit, ICBC said "well, then we'll just cut you a cheque for the 1200 and you'll be on your way."
"No," I said, "I undervalued the car on the transfer papers to save money on taxes."
"But that's illegal!"
"Yes, but I'm still not accepting 1200 for this car."
In the end, they sent an independent appraiser to my place of work - at no cost to me. His appraisal was within one hundred dollars of what I had paid for the car 4 months previously.
ICBC did not report me, and paid to have my car fixed properly.
You are their customer and are paying them for service. The onus is on them to value your car properly. Stand your ground and insist they provide an independent appraiser.