You are not at all obligated to give a detailed statement to either your insurance company or the insurance company of the other driver.
Talking to the insurance companies is actually rarely in your best interest, and the insurance companies are hoping to lock you into a statement to use against you later.
If you talk to an insurance company right after an accident and tell them you aren't injured, but then a few days later you start noticing symptoms of an injury, the insurance company will use your initial words against you.
Don't give the insurance companies the chance to do that.
They lose money by paying claims, so they want to b sure to pay out as little as possible after every accident.
Typically all you need to report to your insurance company is that you were involved in an accident, and then when and where it happened.