With a group like that, I wonder if federation really brings them advantages.
With a closed group a central server might be just fine.
Anyway, yeah, ActivityPub was pretty much built with the idea that everything published through it would be effectively public, so anything built on top of ActivityPub would share that feature by default. This includes Mastodon, Lemmy, and all of the other Fediverse interfaces.
It was a design decision of ActivityPub.