When you install the Command Line Tools, make sure that you start the version of Xcode that you specified in this step. Where xcode_path is the path to the Xcode version you want to use. I did so, but whatever script had displayed the message seemed to have hung because the (uncancellable) message wouldn't disappear, and the installer wouldn't.
When I woke up, the installation had popped up a message saying to close Xcode first (doh!).