I've just corrected the documentation to say "except permissions" rather than "except edit permissions".
By default any new page inherits the same role permissions as its parent page, so if the parent page has departmental view and edit roles any new child page will inherit the same roles.
Only admins and content admins (and site editors in a multi site installation) can change permissions on pages or feature instances.
Hiding is not a security feature, it is cosmetic and only removes it from the menu, it does not protect the page.
If you want a private section below a department level page you should have an admin or content admin setup the first page with the restricted view roles then dept editors can create pages below that with the same permissions.