You can send the URL to any people You want. The thing with the private content is only to protect personal infos of living persons.
If You want to present Your family incl. living persons to somebody, You must invite him/her to Your family site. Then thisone can see all infos.
Additional tip: if You want to protect family site members from chenges in the family tree, go to Family tree .. Manage trees. There You will see Your family tree (or trees) and on the right side of the corresponding tree click on Edit tree settings. Now You can adjust the edit permission of the tree.
Hope this helps .. and hope I did understand Your question