I want to allow all users to invite their friends to the site by email, so I have selected Allow email invitations to be sent by: All users.
I don't want users to be able to see the list of everyone else on the site that isn't a friend, so I have set the Limit group invitations dropdowns to friends only, so they can only see their friends list.
But with those two options set, the invite by email option has vanished and essentially I'm using the built in BuddyPress invite screen. The email invite only shows up when I allow them to invite non-friend users too.
I'm running it on a multisite install in case it's an incompatibility issue.