Edit: Oh yes, a quad-core ARM-based Android 4.4 Tablet that I own, mysteriously had something installed, that seems to have nearly-full privileges in Android, and cannot be removed. I've tried factory restores, they don't get rid of it. I know for a fact that I didn't install it.
I did install an .APK from somewhere other than the Google Play Store, and this software did not immediately appear alongside the software I installed. So either, the APK was booby-trapped, and loaded this malware later on over Wifi, when I left the tablet in standby, or it came in through a system update somehow, when it was in standby over wifi.
(Do Android tablets suddenly initiate updates when connected to Wifi?)