When "Use site-specific assets" is checked in Admin - Config - Manage Websites and saved, an item is created under the start page called "For This Site"

As seen under   Admin - Manage Content 

When "Use site-specific assets" is then unchecked, and saved then the name of that item is changed to SysSiteAssets but not removed.

Admin - Export Data works correctly. However if the Start page does not allow the SysSiteAssets type of content as an available content type then importing to another instance will fail.

E.g. My Start page has [AvailableContentTypes(Include = new[] { typeof(StandardPage) })]