Solved! Go to Solution.
configOptions = {
...
webmap: "",
appid: "",
// Optional list of authorized application or web map owners
// Has to be specified when using appid or webmap url parameters (e.g. ["user1"], ["user1", "user2"])
authorizedOwners: [""],
...
};
Hypothetically it might be possible to create a storymap with REST services hosted on your server, make the app "public", but control access through the REST service. Then download the app, and host it on your web server.
I'm not sure if this will work or not, but I have a similar need (i.e. don't want full open access, but don't want access limited by named users in ArcGIS Online). If I can get it working I'll post back here/