Eric, I have same question and I believe OP is correct. App login does not work with private content . Limitations of App Login | ArcGIS for Developers Currently ArcGIS Online does not provide a way to share Web Maps/Apps with external clients (non-AGO users) without sharing the content with Everyone. This is a much needed feature and has already been requested by many: https://community.esri.com/ideas/11655-client-facing-password-for-shared-apps . I could not find a work around for this and will really appreciate if you can share how to make this happen.
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