It seems that you have to specify every user, or specify a group that those users are in, so that they can start a Business Process. It does not default to allowing everyone to submit that form if it's published.
The "everyone" group was something you could add in Forms 9.0, but doesn't appear to be a valid option in 9.1. How can I make it so all Named users in a repository can submit a form that has been Published?