Interactors do not have publishing rights. From http://onlinehelp.tableau.com/current/server/en-us/help.htm#users_site_roles.htm:
Interactor: Interactors can sign in, browse the server, and interact with the published views. It's important to note that specific views, workbooks, and projects may have been published with permissions that restrict a user's capabilities. Permission settings can be edited by the workbook author or an administrator.
Interactors can view workbooks and can interact with views. They are not allowed to publish to the server.