My wife and I were travailing. Another car passed us, cut in front of us, and hit us. They are claiming we hit them.

If your car hit the back of theirs, the insurance company will usually start with the assumption that you were at fault. That makes this an uphill battle, but the other driver’s report does not settle it. If they cut directly in front of you and caused the collision, you need evidence showing that you had no reasonable chance to avoid it.

Give your insurer a clear account of the lane change, including where both cars were and how the impact happened. Your wife can give a statement too, but because she was in the car with you, I would focus on finding independent evidence. Dashcam footage, video from a nearby business, or another driver who saw the other car cut in front of you would help most. Keep photos of the damage to both cars as well.

Without that kind of evidence, it may be difficult to overcome the other driver’s claim that you were going too fast. If the insurer finds you at fault, ask what it relied on and whether it considered the lane change and any evidence you provided.