Legal Question in Insurance Law in California

An insurance company can investigate insurance fraud. However, an insurer investigating fraud does so through a special investigations unit -- "SIU." When the insurer's SIU investigates, it must report the fact of the investigation to the California Department of Insurance.

If this is being handled by an ordinary claims adjuster then I doubt that they are investigating fraud.

If they are not investigating fraud, your credit profile, banking and credit card history are protected private information and should not be required to adjust a theft claim.