I thought you might be accessing the layer without signing in, for example, via a web app from a template.
Did you disable the Data capability on the one layer when publishing? (i.e., Map, Data Query)
What are the data sources of the layers the same? for example, both shapefiles, or from geodatabase?
If you don't feel comfortable sharing a link to the layer publicly, you might consider calling Esri Tech support and have them take a look.
Thanks,
Mike