Further, they do not need your statement. They already know what happened. The purpose of that statement is to obtain information from you that can later be used against you. Do not fall for the line that they are only looking for the truth . The simplest, most straight-forward, and truthful of statements is always susceptible of being distorted by the devil.
Answers take their meaning from their questions.
Be truthful but avoid making categorical or detailed statements that may set you up to later being proven wrong. Try to play for time to see a competent and experienced lawyer. You generally will have an obligation to cooperate with your own insurance company and provide them with a statement if they want one. Even then, understand that insurance companies do cooperate, and exchange information, with each other. It is human nature to ask that question and it is human nature for the injured person to try and reassure those about him that he is ok, ie.