On OSX 10.6.8 (outdated, yes, but probably applies to more versions)
With a fresh install, use the dashboard link to install the Android SDK.
When it requests a path, enter ~/.android (or any path beginning with ~)
Install as normal
SDK is installed to /Applications/Titanium Studio/TitaniumStudio.app/Contents/MacOS/~/.android
SDK directory is stored as the path entered, so Titanium Studio cannot find the appropriate SDKs without tracking down where the SDK Manager installed it and entering that directory in the preferences.
SDK is installed to ~/.android (more specifically: /Users/[username]/.android
or at least SDK is installed to /Applications/Titanium Studio/TitaniumStudio.app/Contents/MacOS/~/.android and the directory is set to the same so that Titanium Studio recognizes the installed files.