Is it considered a private API to use App-prefs:root?
Yes. The only legal way to open Settings is to use UIApplicationOpenSettingsURLString.
My app just got rejected because of this, so yes, it is considered as private API :)
Here's the rejection notice from Apple:
Your app uses the "prefs:root=" non-public URL scheme, which is a private entity. The use of non-public APIs is not permitted on the App Store because it can lead to a poor user experience should these APIs change.