Hi,
Just wanted to add a few things to help anyone coming across this post.
If we're sharing our Story Map publicly all content in the Story Map needs to be shared publicly in order for non-signed in users to access it. This includes all Web Maps, Layers and Web Mapping Applications within the Story Map. I believe there's also a consideration for sharing premium/subscription content publicly.
There's a great tool in the My Stories section of the Story Maps website that checks your story maps for issues such as content not being shared publicly. We can use this to help identify content that is not shared at the same level alongside other issues. Worth noting that it won't check embedded applications - so if we've added an app like Spyglass into a Story Map we'll have to ensure that the embedded Spyglass app (and its Web Map and Layers) are also shared accordingly. Of course we can also manually view all the items back in our My Content as well (I try to put associated content in the same folder, where possible).
I disagree in that Story Maps are less 'reliable' than Web AppBuilder. They each serve their own purpose. The Web AppBuilder is definitely a go-to for when we need to focus on a single Web Map, add select widgets and theme our application. Story Maps and other configurable templates give a lot more options, including the ability to use multiple Web Maps and even embed other Web Mapping Applications. These additional options do add a level of complexity - it's a lot easier to check sharing permissions for one Web Map, app and its layers, than a Story Map with multiple Web Maps or embedded apps. That's one of the reasons Story Maps have a check tool available.
Chris