Who else can invite members apart from the Community Managers?

Any active member of the community is able to add new members. 

The Community Manager's "Manage" screen will keep track of who invited each member and when. As a Community Manager, you'll also be emailed when a new member joins by accepting somebody else's invitation, and they will be marked as "Confirm" on the Manage page until you've confirmed that you've reviewed and confirmed they are eligible, at which point they become and "active" member like the rest. 

If you ever have cause for concern that a member should not have been given access, you can delete any of their posts or delete the member completely from the manage page.