still need details i would think if you in fact had insurance and the cop still had your car towed on top of that you told him a flat bed and he still had a normal wecker pull it i would say either:

a) insurance will have to pick it up for not sending more accurate records to the state w/ your info

b) state/county/city cop will have to pick up damages b/c there were prewarned and insurance was on the car

c) wrecker for fucking it up