Who is asking the question?  A director?  A member?  The executive director?  And what is the discussion about?

Realizing that there are many different perspectives may help people understand that there is no necessarily single right answer to the question.  The question implies that talking about the exec’s behavior in a public setting is wrong.  But the discussion could be critical to the organization’s well being.

I am one who thinks that may organizations go too far in attempting to keep things “confidential,” especially from the members of a nonprofit organization.  Presumably if the exec is ill, you may not want to (and may not be legally permitted to) disclose the nature of the illness without the exec’s consent.  But if you have just reported the exec to the police for stealing from the organization, it may be a necessary first step in correcting the organization’s governance situation.

People may not necessarily agree on where to draw the line on what is appropriate for discussion “in public.”  But this question does not arise in a vacuum, and the person raising the question, who apparently thinks the current range of discussion is not appropriate, ought to raise the issue with those who the questioner thinks are going over the line. 

Officers and directors have a fiduciary duty to the organization and may want to get feedback from the members they represent.  Members may want to know if their elected representatives are fulfilling their fiduciary duty.  The exec may simply want to be in hiding to avoid difficulty in moving on to a new position, unless, of course, the discussion is about the exec’s great success in the organization’s last major project.  Talking the issues out before they arise, or as they arise, will help people come closer to agreement on the appropriate range of discussion.  But don’t expect a complete consensus.  There are legitimately competing interests here.