Edit: Sorry, misread. It goes over LAN if possible.
I think that is not true. The idea of Home users is that they don't have to pay anything if you already have a plex pass. You may verify that in Plex forums.
Sorry, when I said "Home Owner Account" i should have been more specific, and said the Plex Pass Account.
I guess each family needs to evaluate the $40 per year for a single Plex Pass, or for each family member device paying the once-off $5 'per device' cost.
As you pointed out, only the Home account owner can add / delete content from the shared library, so maybe it is better for each family member to have their own Plex account, and share their libraries with each other.