Invoking Aahz's Law

In which it is said that the best way to get correct information about a subject is to post incorrect information about it.

I've just been playing with LJ friends groups. One of the features of friends groups is that you can set a group to be "private", which as nearly as I can tell, does nothing at all. I would think that the existence of a private group would not be visible to anyone not logged in to LJ as a member of that group, but that's apparently not true. As a test, I just created a private friends group "nyrsf_cabal" featuring the NYRSF staffers whom I know have LJs, and the contents of it are visible to all.

I would expect that a "public" group would somehow be visible on my User Info page, but that, too, appears to be untrue--the public group "castle" contains supergee and nellorat, but no info about that shows up on my User Info page.

Thus, I posit that "private" and "public" is a meaningless distinction. What say ye, assembled wisdom? What am I missing?

Since that worked so well

I will now say that I cannot find a way to read eBay listings with an NNTP client. I would very much like to be proven wrong.