Hi Joshua,
Thanks for the message. I just tested this with a few story map apps and other configurable apps, but I'm not able to reproduce the issue you are describing. When I'm logged in as another member that is a member of a collaboration group I see the "Configure app" button on the item page for items shared to that group as expected.
Could you please check to see if this is still the case? If you still see this issue I would recommend contacting Esri Support for further assistance.
Owen
Owen Evans
Lead Product Engineer | StoryMaps