The short answer to this question is, of course not. Some insurance companies are pretty aggressive when they are reaching out to someone who has been involved in an accident. The first thing the adjuster wants to do is to try and get a little bit more information about the case. And, the way they usually represent themselves is in a way that seems like they are helping you but the bottom line is they are not, so watch out for these tactics.
Remember the other driver's insurance company is operating on a very scripted plan to try and get your case settled quickly and for as little money as possible. The number one thing they want to do in order to accomplish that goal is to try and get you committed to a certain set of facts in a recorded statement as soon as they can.
The insurance adjuster is persistent in wanting to get a recorded statement because so many times people commit themselves to facts or commit themselves to how they feel that later turns out to not be as reflective as to what really happened in the accident or how the victim actually feels.
Don't fall into a trap of feeling like you have to give the adjuster a recorded statement because the bottom line is you have no obligation to do so.