If you encounter the Google Groups error
No new people were added to the group One person is already a member of the group. The provided email address might be a primary, secondary, or alternate email address of this person.
when trying to Direct Add or Invite a user to a Google Group, but there are no users in the Group which could possibly have alternate, primary or secondary email addresses that conflict with the address you're trying to add, here's a workaround to this apparent bug in Google Groups.
Change the permissions on the Google Group manifesting this problem to allow people to apply to join the group :
"Manage"... "Permissions"... "Basic Permissions"... "Join the group" : "Anyone can ask"
Then have the user who you couldn't add or invite, go to the Google Group and click the "Apply for membership" link. Then approve their Join Request and they're in.
Afterwards, set the "Join the group" permissions back to "Only invited users" if that's what you had before. Here's where I reported this bug
I experienced this problem with two different Google Groups and three different users and was able to get them all added by this method.