Generally, no. Many times, the questions are phrased so that the answers can be misconstrued or are misleading. Sometimes we give the opposing insurance company a statement, after investigation and in the presence of legal counsel. We only do so in cases we regard as very strong, and that should settle immediately. The answer is different when the inquiry is made by your own insurance company. Most insurance policies require that the insured cooperate fully with the insurance company. Failure to provide a statement can be deemed non-cooperation, and void the policy.
If I am in a car accident and the insurance company for the other driver asks me to give a statement, should I give it?