This may be the case in Virginia. In Connecticut the corporate officers and members of an LLC are personally liable for their tortious conduct (Neglience is a tort). Salmon VS. Richardson and Scribner VS. O'Brien. If you need the reporter page and volume numbers  let me know.

Since they are personally liable it would make sense to make certain that they are insured. If your insurance carrier feels that you are adequately portected under your policy in Virginia ask for it in writing. If he is right he should have no difficulty giving you a certificate of insurance indicating that you are personally covered under the policy. If not, you may want to look into additional coverage for yourself. Better safe than sorry when someone asserts a claim against you.