My parked car got hit by a shopping cart. What advantage is it to me to admit I was sitting in the car at time of accident?

Depending on your policy, it might make a difference. Property damage to your car as a result of a driving accident is covered by the "Collision" coverage under your policy. Damage caused by an outside force when not driving may be covered by the "Comprehensive" coverage under your policy. The coverage limits and deductible amounts under these two coverages may be different. So, check two things. First, look at the policy language to try to determine whether this event is covered by "Collison" or "Comprehensive". Second, check out the deductibles and limits of these two coverages. Indeed, it may turn out that you don't have one or the other of these coverages, so the policy language becomes even more important.

As I am not licensed in your state, I can only provide you with some general guidance. You have a duty to cooperate with your insurance company in the investigation of the incident. You should tell them the truth, whatever it is. This type of incident is usually covered under your comprehensive coverage with your own insurance carrier. However, if you know who the person was who caused the car to collide with your vehicle, you could sue that person.