Publishing (including story download), is determined by your subscription type. There's a number of options available.
If your workspace has publishing enabled, then access to individual publishing locations can be controlled according to teams and individual users and is set by the workspace owner or team leaders. It is up to the workspace owner and/or team leaders to decide who can publish and to which locations.
You can see who in your teams can and can't publish to each location by going to the team settings page. You'll find a table of all the team members and their role within the team (a leader or member), and columns for each publishing option available to the team with checks for each member who can publish there.
If your publishing permissions need to be changed, contact your team leader.
If you are a team leader and wish to change publishing options for members of your team, you can do so by simply clicking on the checks or slashes to change the permissions for any user within your team.