Did you know Freddie Mac and Fannie Mae are private?

I feel like a bit of an idiot right now, but I'm fairly sure that most people still think that Freddie Mac and Fannie Mae, the two enormous corporations now at the center of the credit/loan crisis, are government agencies or, at the very least, public-private companies heavily controlled by the US Federal government.
I was wrong (and if you are one of my presumed majority, so were you).
Freddie Mac and Fannie Mae are "government-sponsored enterprises". Now, the official definition for what that means is pretty long, but the essence of it is:

The term "government-sponsored enterprise" means a corporate entity created by a law of the United States that has a Federal charter authorized by law; is privately owned, as evidenced by capital stock owned by private entities or individuals; is under the direction of a board of directors, a majority of which is elected by private owners...

[via the US House Office of Law Revision Counsel]

This assumption of mine led to my comfort with several recent developments that I am no longer as sure about. For one, it is not absolutely clear to me that the taxpayers should be massively bailing out any more privately-held companies (Bear Sterns being the first) who seemingly ruined their houses themselves (see NYT article, At Freddie Mac ... Warning Signs). It again seems like a bit of smoke and mirrors: let the populace think that we're part of the government so that they don't think twice about having to bail us out and we have an easier time of getting low interest rates on capital.
Ultimately, having already made my peace with bailing out Bear Sterns, I am in favor of helping out Freddie Mac and Fannie Mae as well (perhaps even more so, as, through them, the government is helping out a lot of borrowers who are having trouble making payments on their loans' principal and accrued interest). I just wish I had known I am helpint to bail out another series of privately-owned corporations...