Do I have to give a statement to the other driver’s insurer?
No. You have obligations to your own insurer, including the duty to cooperate and to submit to an examination under oath where properly demanded under 11 NYCRR 65-1.1 and 65-3.5(e). You have no comparable obligation to the other side’s carrier, and a recorded statement given to an adverse adjuster becomes a document the defence can use.