As my tablet doesn’t support Google Play, I visit the forum at 4pda.ru to download APK files. The topic about AMS is here: http://4pda.ru/forum/index.php?showtopic=289024
First I read this message: http://4pda.ru/forum/index.php?showtopic=289024&view=findpost&p=24285830
Translation into English:
The new version required to install Google Play (Google+, advertising and other strays) that a month ago I gladly took down - as if it can't work without them. What a Masonic conspiracy, eh! I fell for the ruse and installed them. Tomorrow I'll take them down once more and will see if it works.
A bit later the user added: http://4pda.ru/forum/index.php?showtopic=289024&view=findpost&p=24311915
I demolished the services as intended. Then I updated the bases, scanned my applications, looked into my Anti-Theft settings - everything works, Google Play services are no longer required. It was a single Google's PR action, I suppose.