If you read a little farther down that page you'll see it says that CGI::Carp does this for you. It should work normally. There may be something about CGI::Application or this person's config that is breaking it.
Well, exceptions send a 500 to the browser and get logged to the container's errorlog in my mod_perl setup running under either PerlRun or Registry, so without CGI::Application, it's not working for me either now or in the past.. fatalsToBrowser doesn't work out of the box. You still have to write something to handle exceptions and include a reference to it by altering %SIG.