Google has added a new condition in Google Play Developer Program Policies, making self-updates by apps downloaded from Google Play a violation. This is not something unheard off and one recent example of such action was Facebook, which recently pushed an update to its official Android app directly and outside Google Play for select users.
From now on, if any application, which has been installed using Google Play, tries to push app updates outside Google Play, it can be removed from Google Play. So, developers be careful.
Here is full sentence from the “Dangerous Products” section of Google Play Developer Program Policies:
“An app downloaded from Google Play may not modify, replace or update its own APK binary code using any method other than Google Play’s update mechanism.”
You can find the full document of Google Play policies here.