For the sake of posterity, I'm posting this. Hello Googlers!
Ok so it turns out I had the remnants of a virus on my machine. The virus is long gone, but when I did a "netsh winhttp show proxy" it showed that I was pointing to localhost:7171. Fortunately whatever virus did that is now gone.
So here's the deal. First of all, I'm NOT responsible for what happens to your computer, I'm just offering advice that worked for me. Anyway, If you get this error and you've gone through everything else to no avail, fire up a command prompt. That is, go to Start--Run and type "cmd.exe" and hit enter.
At this point type "netsh winhttp reset proxy" and hit enter.
Enjoy your new Windows updates.