I've had a similar issue, the paths in $PATH were correct, and when I browsed to my local bin folder:
cd /usr/local/bin/
I could see the subl file / shortcut.
After pening this folder in finder with:
open .
I could see the icon looked incorrect (white), perhaps a previous version. Double clicking it also gave an error, so I manually copied the subl file over, after expanding contents of the Sublime Text 2.app.
If you drag the file over, it will create a shortcut, if that doesn't work then first duplicate the subl file in its original position, then drag over the duplicate and rename correctly. Or just give the correct permissions on it.
Hope this helps