Skype showing me as online - after stopping app and even after device shutdown?
OMG, I have found the following posting: http://community.skype.com/t5/Security-Privacy-Trust-and/Skype-invading-and-changing-people-s-online-status/m-p/2961695/highlight/true#M28546

According to above the "always on" concept was a deliberate decision by Microsoft:

(...) we have changed the way online status presence works:
(...) we are showing you as online to your contact even when you left or
force killed the app on your mobile phone (...)


They admit that certain scenarios need fixing:

Now we've identified a few scenarios where this is simply misleading:
 - you've switched off your device
 - you've disconnected from the internet (e.g. by switching to airplane mode
   and you are somewhere mid flight)

In these occasions you are right now still shown online and we are working to
make Skype presence indicator be meaningful in these scenarios as well.


This is just so weird.
They should certainly make it configurable.

For now the only way to disconnect is to manually "sign out".
Quitting the app isn't sufficient. Shutting down the device is neither.

Status Update (2015-08-15):
The problem is back. And it's even worse!
Even though i manually sign out, quite the Skype app and shut down the Android device I'm still being shown as "online"!
Observed with: Skype 5.9.0.14047 @ Android 5.1.1