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