According to bug ticket #12267, this was fixed. However, I was able to reproduced this bug once again on latest 3.0.6. I wasn't the original owner of the ticket, so I can't seem to open it again. Therefore, I started a new one here. Please merge if necessary.
To reproduce the problem:
1. I gave all Registered Users permission to change their own avatar.
2. Users have changed their own avatars by either uploading their own image, uploading from URL, or picked from local avatar gallery.
3. I set some users' default group to custom groups I created.
4. I set the group avatar for the built-in Registered Users group.
5. All users with the built-in Registered Users group as default have their avatars changed to the new group avatar I just specified.
6. I changed the built-in Registered User group avatar again by checking the "Delete Image" check box and submitted the change.
7. All users with the built-in Registered Users group as default now have no avatars.
P.S. I also agree with Ida (see original bug ticket) on the default behavior of the group avatars. Perhaps it would be nice to give a check box option as to whether to use group avatar as a "fall-over" avatar and/or overwrite existing users' avatars when changing the group avatar?