Presumably you are “allowed” to tell the member whatever you want.  But why would you want everything kept confidential?  Your basic financial information is eventually public information.  If you are soliciting charitable contributions, you may want information to be made public to increase your donations.  If you are dealing with a social club with many members, it isn’t reasonable to believe that all of them will keep everything confidential no matter what you ask.  If there is stuff that is truly confidential, don’t disclose it to the member, at least not at a public membership meeting.

Ultimately, of course, if the member doesn’t like your information policy, it can change it.  As the sole member of your organization, it can probably remove the current board members of your organization and replace them with individuals who will adopt an information policy more to its liking.  That’s the nature of being a wholly controlled subsidiary. You might want to work with them to discuss what is really important and whether you can reach an understanding on what you will generally discuss in public.