ArcGIS Hub does not support DCAT for private sites. As user report that this is new behavior, perhaps a bug was recently fixed in which, Hub previously exposed the …/data.json endpoint for private sites when it should not have been doing that in the first place.
Also, looking at the DCAT configuration for the public site referred to in the bug report, the email address points to a field that does not exist (in the metadata for the item). If the user wants that to be valid, ensure the metadata for the item actually contains that field.
We would be willing to work with user to see what is exactly going on in their particular configuration or scenario.