According to the documentation on ArcGIS Hub, the option to download data as a file geodatabase (FGDB) should be available only for hosted services. However, it is currently available for non-hosted services as well.
Hub and the corresponding documentation around this have changed since the bug was initially observed and reported.
This page: https://doc.arcgis.com/en/hub/content/enable-file-geodatabase-downloads.htm is no longer part of Hub webhelp.
The page https://doc.arcgis.com/en/hub/content/data-download-settings.htm#ESRI_SECTION1_4A05EA4751764F1B882A235DEB00CCF9 now states that FGDB download is only available for feature services hosted in ArcGIS Online.