How do we request publish_actions in Facebook for a private app

Question

My Android app connects to a Wifi camera, grabs a picture and asks the user his Facebook login to post the picture on his wall. Publishing works very well with my developper account ; however, to make it usable by any user, I need to get the publish_actions authorization for my app.

I've submitted a request to the Facebook team, enclosing a video of the picture posting workflow, the privacy policy, a 1024x1024 app icon, and so on... but the team replied by with a deny for the following reason: they could not reproduce the publishing steps.

This is absolutely normal since:

• The app is private, not published on any store
• The app requires specific Wifi camera (with specific brand and model) to work properly and publish a picture on Facebook so even providing the private APK to Facebook wouldn't solve the problem.

They tell to fix the issue and make an other attempt. How do I fix this issue, though?