The export mirrors exactly what is on screen: filters, search and team scoping. Every export is logged, with its author, its volume, its period and whether or not it carried contact details. Simply viewing contact details on screen is not: what is traced on personal data is its EXIT, not its display.
The right to see leads allows the export; a second capability decides whether it contains CONTACT DETAILS. A user who lacks it gets a normal file, with its columns and rows, but with no name and no phone number. Nothing fails, and that is exactly why you need to know before passing the file on.