I have been struggling with this authentication issue for some time and slowly working toward moving to AgsGIS Server Authentication however I have just seen that this issue has somewhat changed. Positivitly I hope.
The article referrenced has been updated and now states support for Web Tier Authentication:
ArcGIS Online supports ArcGIS Server authentication, including web-tier authentication such as Integrated Windows Authentication (IWA) and a public key infrastructure (PKI), for adding and accessing secure services. When you add a token-based secure ArcGIS Server service to a map, ArcGIS Online prompts you for credentials every time you access the service. Credentials are not stored in the map. ArcGIS Online takes care of obtaining a token for authentication; there is nothing additional you need to do. You should not attempt to append a token to the URL when you add a service to a map.
The map viewer, Web AppBuilder, and the configurable apps support editing feature services secured with web-tier authentication. To take advantage of this support, administrators must configure trusted servers that allow ArcGIS Online to automatically pass through credentials.
I am workign through this new position now but wanted to share this with others who had been hitting this issue.