[geoutah]

Yes, the theme is disabling this basic functionality.
I think it’s this: http://pastebin.com/DDFtUfwQ (code available by clicking on link).

Do I just delete this code…? Suggestions?

[geoutah]

When you create the group, it can be a private group. Try creating a test group that’s private and play with it. Create a test user and try it out.

I would explore plug-ins to see if there may be a fix there for you. I’ve never tried to have this level of specific customization, usually plug-ins are the answer.

Some of this may be theme specific.

[geoutah]

First question: is this a Buddypress theme or just a WordPress theme?

If this is not a Buddypress compatible theme, this would result in the theme not working.

Try installing the theme first, without Buddypress. If it works, then you know it is not Buddypress compatible.
I would carefully review the theme documentation and follow the installation and activation instructions. Most of the problems I’ve had start there.