Public figures are not immune to being deposed if they are a Party in a lawsuit. In Arizona, the testimony of parties or any expert witnesses may be taken by deposition. See Rule 30(a) of the Arizona Rules of Civil Procedure.
Ms. Brady has a good answer. Public figures can be sued and their depositions taken as a part of the lawsuit.
This posting is intended for general education and isn't "legal advice." It doesn't create or evidence an attorney-client relationship. You are encouraged to engage an attorney in the pertinent jurisdiction for confidential legal advice on matters of any importance.
Public figures have no special immunity. They do often have expensive and aggressive attorneys.
We do not have a client/attorney relationship until you make an appointment, we discuss your case face to face, I accept a retainer, and we explictly agree to enter into representation.