There's "View Summary Data" and "View Underlying Data" permissions. Did you try those? I don't know what permissions list you looked at (provide the URL). If the permission is denied then the user would not be able to see nor download the data. Technically, if they could see the data they could take a screen shot of it and thus "export" the data so this permissioning makes sense.
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This is the list I've got from the Tableau Server Administrator Guide (http://downloads.tableausoftware.com/quickstart/server-guides/server_admin6.1.pdf?keywords=Admin%20guide) is below. All the other permissions are in the permission section except Export Data. So is there another place I haven't looked at or doesn't it exist except in the export button and the only way to stopping it is with stopping them to see the underlying data?
Finally, when someone publishes a workbook to the server, he or she can allow and deny specific
capabilities to further control who can access the workbook. The following capabilities can be allowed
or denied to individual users or entire groups:
View - See the workbook on the server.
Write - Edit and republish.
Delete - Delete the workbook from Tableau Server.
Filter - See and interact with filters that are published with each view.
Add Comment - Add comments to the view.
View Comments - See comments associated with the view.
View Underlying Data - See the raw data behind each view.
Export Image - Export and save the view as an image file.
Export Data - Export the aggregated data as a comma separated value (CSV) file.
Download File - Open the workbook from the server using Tableau Professional.
Share Customized - Make saved customizations to a view public for others to see (users can
create custom views using the Remember my changes option).
Move - Move the workbook between projects.
Set Permissions - Modify the permissions.
To make it easy to assign common combinations of these capabilities, Tableau Server comes with
some pre-defined permission roles. Select one of these roles when adding permissions to see the
capabilities it allows. Refer to the Setting Permissions topic in the online help for more information
about assigning permissions.
That link you're referencing is for version 6.1. Use the link I provided as it's the most current version. Version 8.0, 8.1 permissioning is the same.