Basically all Documents are created as Public, so if you want it to be Private, you then have to edit it.
Either Geni should find a way to not show to non-family members the creation of the Document under "Activity" when it has been changed to Private -- or if this is impossible - how about changing things so Documents are always created as Private, and have to be changed to Public -- then could the General Geni-Public not be shown the announcement of their creation if they were left as Private?