Insurance companies are usually quick to call the injured person after a car accident. Injured people are usually interested in talking with them and being cooperative. Nothing wrong with being cooperative, right?
Actually, it is not in an injured person's best interest to talk to the insurance company of the person who caused the accident (you have an obligation to cooperate with your own insurance company, but this article refers to talking to the at-fault insurance company). The injured person probably was interested in cooperating with the insurance company and talking to them in order to speed up the repair of the damaged car. This will not speed up the repair. Usually the insurance company will not agree to pay for the repair until they see a police accident report and speak with their own insured.
The injured person also thinks “I'll talk to them since I have nothing to hide.” While it's true you have nothing to hide, you also have nothing to gain. The insurance company wants to talk to the injured person in order to protect the insurance company's interests. They don't want to talk to the injured person because they care about the injured person or because they are genuinely interested in their problems.
The insurance company will usually record the phone calls. They are hoping you say something that might help them with the claim. Maybe they'll ask how you are feeling and you say “I'm …okay”. You might mean that you survived but the insurance company will get a transcript of that phone call and a year later argue that the surgery you had from the back injury from that car accident wasn't related to the car accident because you said you were “okay” when they talked to you. Maybe in the phone call they'll ask what your injuries are and you'll say “my back hurts.” As time passes maybe your back improves and it is your shoulder that has a serious long-term injury. The insurance company will use that phone call to argue that you never mentioned anything about your shoulder so maybe your shoulder injury isn't from the accident.
The at-fault insurance company is not on your side. They are not calling you to help you or protect your interests. They are calling you because getting you to say something on tape that might hurt your later on is how they handle the claims process. Before you talk to an insurance company, speak to a personal injury lawyer.