Hit a tire on the freeway during a pile up accident

We just hit a tire in the road due to a car accident on the freeway. It’s night time so it’s dark and the part of the freeway we were on was not well lit. We saw a stationary car in the far left lane and a short of cars behind it when we drove past, but it didn’t look like a car accident at that point. Seemed like a car was just stalled and it must have just happened since there were only a few cars stopped behind it. We passed the car without seeing an accident, but about 10 seconds later we hit the tire in the middle of the road. We didn’t see it until we were right about to hit it. We immediately pulled over in the shoulder and waited for the cops. While we waiting for the cops to show, about 6 other cars either got into accidents or hit debris. The cop told us that car lost the tire, stopped, and then the car accidents happened as a result.

The cop said that if we file a police report, our driver would be considered at fault because the tire was stationary at the time we hit it. He said if we do not file a police report, our insurance would cover it. That feels really weird to us all. Why would filing a report change whether we were at fault or not?

My main question is – are we at fault for this accident?