Within the HIPAA plugin, hidden fields are processed by Gravity different that other fields (single line, as an example). If you need one of the Merge Tags in the Default value of a Hidden Field it will be saved to the form. However, it will not be saved in the export.
If you need the data in the export, you would need to use single line field (for example) and mark the field as hidden. In this case it will be hidden on the front end, but the data will be save to the form and will be available in the export.