Affiliations other than admin and owner cannot invite to members_only rooms
This is explained in the paragraph:
If the room is members-only, the service MAY also add the invitee to the
member list. (Note: Invitation privileges in members-only rooms SHOULD be
restricted to room admins; if a member without privileges to edit the
member list attempts to invite another user, the service SHOULD return
a <forbidden/> error to the occupant; for details, see the Modifying the
Member List section of this document.)
https://xmpp.org/extensions/xep-0045.html#invite-mediated