The intro text does not appear, and the image shown is the default image (which our template shows when an article does not have an image). But, the article title, author and tags still appear.
That's working as intended then.
This is not what I was expecting... is there a way to make it disappear altogether from the Category Blog page?
No, it's not meant to completely remove articles from the view. It shows a minimal amount of content so you can generate a lead into a sale of a subscription.
To hide them completely I would have different menu items for different users and use ACL. So for example a menu item that filters out those articles (you can use Tag filtering in Joomla for this) and a menu item that shows them. When a user subscribes you can give them a special usergroup for this. Now you have 1 menu item accessible to subscribers and 1 menu item that isn't.