By example, if I want to save a picture from Safari, I click on the picture then the "Send to icon", then "Save to FIles". On that window, "Add" option is grayed out, if I click "On My iPad", nothing happens.
There is an app we are using at the job where we can consult documents, downloading says documents is the same as in Safari.
The two options are check :
Allow documents from managed apps in unmanaged apps (iOS 7+)