Bonnie,
Ah, ok -- you could simulate that by embedding a map using the simple embed app URL that's shown when you share a web map (rather than browsing and picking a map as you normally would). Just replace the webmapID in the URL with the ID of your web map and in your Map Journal section configuration make sure the "Unload this content when the reader navigates away" option is ON. Whenever someone goes to another section and then back to that section that app will reload and give you the original extent.
https://www.arcgis.com/apps/Embed/index.html?webmap=272b375db27d494e9decb5f75fe5db81&disable_scroll=...
You can allow someone to change the basemap by using one of the other configurable app templates (like Basic Viewer or Web AppBuilder) to create an app that has a basemap picker and then embedding that app in your story map. Just make sure to 1) use an https link when for the app when you paste the URL into your Map Journal, and 2) share the app and the map and layers in it the same as your story map. If you don't people may not be able to see all of your story.
Also, be sure that your audience will truly appreciate being able to change the basemap on their own and won't be confused by the options. Often if you are creating a story for a general audience it can be better to simply create a main stage action that switches the basemap for them in the context of the story rather than require them to figure out how/where the basemap switcher works/is.
Owen
Owen Evans
Lead Product Engineer | StoryMaps