That's not what's happening here.
Forget about the first 5 steps. If you install the app and start from step 6, the behaviour will be the same. If the user chooses the Documents folder in the browse window in an app, the app can use the contents of the Documents folder without the need for that permission in the Settings page.
The Privacy settings applies only to access to the Documents folder without the user interaction.
The Privacy settings applies only to access to the Documents folder without the user interaction.