‘Friends’ is a relationship between registered WP users.
Not Groups & Users.
You can extend the Groups component to handle different concepts of Friends, but you’ll need coding skills. Use the Group Extension API.
Yes the default operation in BP groups is that you can only invite friends of your BP Profile. You can change this behaviour with Invite Anyone, which gives you the ability to invite your friends to join the site and for you to invite any BP user to the group, not just your friends.
Another plugin that you might like to think about is BP Auto Group Join, with this plugin you can ensure all new site members automatically join a group.
With these two plugins, you can invite your friends to join your site and make sure they all join your group at registration.