The ability to download layers within a feature service is allowed prior to toggling on the Export Data option.
Last Published: August 7, 2015ArcGIS Online
Bug ID Number
July 28, 2015
August 21, 2020
This issue was not reproducible when tested by the development team. Issues may be given this status when they cannot be reproduced or are no longer relevant in a development version of the software, but a specific fix was not installed to address the issue. The issue's Additional Information section may contain further explanation.
That is by design. The toggle option is for others (non owners) "Allow others to export to different formats."