Why does it appear that I apparently "do not have access to Command Line Tools" in ML?

I just upgraded to Mountain Lion, and now gcc, make, g++, etc. are not found when trying to launch them in Terminal.

So I went to Xcode Preferences, Downloads, and clicked "Install" next to Command Line Tools.

It asked me for my Apple ID, which is weird and unnecessary, but I entered it anyway. Note that I am a registered Mac OS X and iOS developer (so I pay 2x $99 per year).

Much to my surprise, it tells me:

Um, what?! And why is it asking?

It thankfully seems that this was a temporary issue, probably due to the increased load on the Apple servers on Mountain Lion's release day.

I am now able to download the Command Line Tools as before so it seems the issue has gone away.

Alternatively, if you're still having problems, this link worked for me when the "Install" button in Xcode didn't.