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Hi,
In admin Jomsocial Configuration->Privacy -> Group List Privacy is setted to Members, but in front Group pages are accesible without registration. Is this correct?
I noticed some other major bug within this feature, I'm not sure if it's releated to yours, but it's possible. Bassicaly "reset existing privacy" button throws an javascript error, let me consult it with out developers, maybe fixing it will also fix your original issue.
I think you missunderstood the feature, setting this option to members will prevent guests from accessing user's group, from menu below cover image, and this works fine on your site.