It might help to discuss what presence is. A well known book on drawing, "Drawing, Space, Form, & Expression, discusses the fundamental nature of art. According to this book presence (essential to art) gives emphasis to the distinctive characteristics of a thing (in your case an executive) while avoid caricature. It's not just that you must express these characteristics. You must give them emphasis.
So what are the distinctive characteristics of an executive? 1) appearance: a fine well fitting suit, impeccable grooming, and disciplined posture. 2) well controlled speech: sparse words focused on the essential issue at hand, restraint from saying too much else for fear of saying something stupid, and voice: slow, well articulated, and spoken in a low register. No doubt there are others. Again it's not just that you conform to these characteristics. You must find ways to give them subtile emphasis without descending into caricature by overdoing it.
Is this being phony? I don't think so. This gives emotional support to subordinates and increases their confidence in the group effort. These are legitimate core functions of leadership.