The way we have it set up which seems to work is we have a Category created for Social Groups, with "Display in the node list" disabled. It is also set to "Navigation section" of "Default (Forums)", though I don't know that's important at all. Within that category is a Forum (let's call it "Group Discussions") which is likewise set with "Display in the node list" disabled, and "Navigation section" set to "Groups".
No special permissions are set for either the category or the forum within it, but both are set to not display in the node list, so they don't show up on the forum index. If you set either node as Private in Node Permissions in the admin panel, that will cause problems, as I found out.
The Social Groups addon option for "Archive group forums to node" is set to that Forum above ("Group Discussions").
With it set up like that, they're not visible on the forum index, and they show up within the Groups tab as they should.
Of course, if somebody knows or can guess the ID of the "Group Discussions" forum, they can access that forum directly for a list of all Public group discussion forums, but... they could access those by viewing each Public group anyway. I checked and found that it doesn't show Private group discussion forums in that list unless you have forum moderator access or something like that.