You have been in an accident. It wasn't your fault, and you really are not sure what is going to happen. The at fault person's insurance company calls you within minutes, hours, or within a couple of days wanting to talk to you about the accident.
The person on the other side of the telephone tells you that they are so very sorry that this happened, and they immediately want to ask you some questions about the accident. They (should) ask you whether they have your permission to record the conversation. You should ask yourself....
YOU DO NOT HAVE TO GIVE A RECORDED STATEMENT!
Recorded statements are designed for one purpose. To help the insurance company. The questions are all part of a script, which is designed to aid in minimizing the accident, and any associated injuries. Any statement you make will likely be used in the future to benefit the insurance company. My advice with regard to talking to the insurance company is as follows: