In that same paragraph, Dancer::Deployment asserts that you have to have Plack::Runner installed. (Not, mind, that you have to use it) It *sounds* like it might not be, maybe. I've not had the problem you're describing, so I'm kinda feeling around here. And yeah, you'll need to at least set up a rewrite rule in .htaccess, even if you can't monkey with the server Apache config.
The only time I've seen a Dancer script bind on its' own, is when you run it from the command line, so what you're describing seems very peculiar to me.