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.