Chubb group claims to always use OEM parts, some companies will have option to choose when you buy insurance. Do expect to pay more for insurance using OEM parts.
Now I have a question of my own, what happens if the other guy is at fault? Since his insurance is paying for repairs, do they go by his policy or your policy? And forget for a moment about no fault insurance , let's say your car was parked at shopping mall and somebody backed into it , I would think no fault wouldn't apply then.