Notwithstanding the provisions of Article 4.7 (commencing with Section 1125) of Chapter 1 of Division 4 of Title 1, any member or ex officio member of the board who is also a member of another public agency, a county supervisor, or a city council person, and who has in that designated capacity voted or acted upon a particular matter, may vote or otherwise act upon or participate in the discussion of that matter as a member of the board.