How do I only allow authenticated users to interact with Organic Groups "groups"?
I ended up answering my own question.
There is no access control with organic groups which disallows anonymous users from seeing public organic groups.
You can use the "Domain Strict" module and have the website that the organic groups is to be hosted on not allow "Anonymous" users to view that domain.  This is a configuration option with Domain Strict.

This has the desired effect.  The only downside is that your domain which hosts your organic groups will not allow anyone who is not authenticated to view any content on said domain.

To change this go to Structure-->domains-->User Defaults
find your domain that will hold your OG groups and uncheck "Anonymous User"
Click save configuration.

Tada!