Has Geico ever paid on a fraudulent claim?

Tweet

I used to have Geico car insurance; I loved their rates and most the time their customer service was really good. THEN; my parked car was hit by an SUV in the passenger door as my husband was opening it. This happened on private property so the police weren't notified. The guy that hit my car claimed it broke his drive line and cracked his head light. The crack in the head light was already there before he hit us and after he got his gasoline he left the area. We did exchange insurance information. Both Geico and his insurance company claimed that we should look out the back window of out parked car before opening the door. They claim the accident was our fault. When the driver of the suv claimed we broke his drive line they turned the case over to fraud protection. Fraud protection reinvestigated the accident and made the determination that both of were at fault. They paid to repair his bumper but his insurance company would not pay a dime to replace my broken/non-closeable door. I paid $500 to get a door on my car. I have heard that filing a fraudulent insurance claim is against the law. Is this true? What would you do in my case?