The assesor is talking the truth and lying!!
Who OWNS the car ?, you do, if the insurers consider it is beyond ECONOMICAL repair they will call it a write off.
This ONLY means they will not pay the repair bill, as it is more than the car is worth etc.
Firstly you are quite LEGALLY allowe to arrange your own repairs as the car is yours, UNLESS you accept the money being offered to you by the insurer, you can then NEGOTIATE to either accept the money offered, LESS the cost of the SALVAGE(car) that you KEEP from them, most ar emore than happy to do this as it cuts thier costs down, for storage disposal etc.
OR you can say what will you pay me to repair it.
Remember it is YOUR car, YOUR property, NOBODY can write a car off unless you accept the money, it will THEN become the property of the insurance company.
A write off is a scary(for some) term that means nothing more than, "too expensive to repair", bearing in mind it's value once repaired.
tabetha