In a word, no.
Insurance company representatives usually put pressure on car crash victims to provide an official recorded or written statement about the collision, their injuries and medical care, and their experiences with pain and disability following the wreck. While the reps are allowed to ask for this, no law requires the injured person to give an official statement.
The insurance company wants an official statement that they can use like testimony. If things you say after giving a recorded or written statement differ from what is in the statement, the insurer will try to use the discrepancies as reasons to deny settling claims.
If you do decide to speak on the record with an insurance company representative, it will benefit you to first consult with a Virginia personal injury lawyer.