When you get into a car accident and it's not your fault, chances are you can expect a call from the at-fault party's insurance company to ask you about the accident. Often times the insurance company will ask you if they can record your statement. The statement they are asking to record is something they intend to use against you. It's definitely not intended to help you. It is not wise to provide such a statement without a lawyer with you to protect you from tricky questions.
Sometimes the questions they ask are loaded with an answer they want, and if the person answering the question does not catch the problem with the question then they end up answering it. Another problem is that the person answering the questions assumes that the insurance company adjuster is a nice person that is just trying to collect information to process the claim. Often times they don't need a verbal recorded statement from you to resolve the claim, especially if there is already a police traffic collision report that includes the statement you provided to an officer at the scene of the accident.
My practice is to deny the request for recorded statements more often than we provide them, because in my experience it has rarely helped a client to obtain a fair settlement for their claim.