Invited Group Members Aren't Automatically Added to Groups
I'm finding that people who have been invited to groups using the "Send Invites" interface (as opposed to the Invite Anyone/Send invitations by email interface) still need to request membership to the group after being invited. I've had several reports of this and have now experienced it myself several times.
I'm not sure what the user behavior was in such cases -- did they actually click "Accept Invitation" in the email they received? -- but we should test this out to see what is going on.