When you create stories in Draft API, it's possible to not circulate the story, and therefore it's possible to have a list of stories that are in an uncirculated state (either published or unpublished).
Today when that happens, you can find view and find those stories by viewing the default website, even though the uncirculated stories are not actually associated with the default website. This leads to confusion because it's easy to assume the uncirculated story IS associated with the default story.
An ideal solution would be to have an option like "uncirculated" available in the websites drop-down field to display any uncirculated stories. This would avoid the default website association confusion and create a clear visual for the current state of your stories.