Any ideas on how to fix this bug/feature of Blender? How can something so simple like selecting another action mess with my work?!
It's not a bug, for the action called TestAction.001 you can see that a LocRotScale track has been created, it means that, additionally to the keyframes you've created for the bones, you've created some keyframes for the whole armature in Object mode. And if you unfold this track you'll see that you have Scale keyframes as well as Location and Rotation keyframes. So delete the whole track, then, as it has changed the size of your armature when you've selected it in the Dopesheet, just select the armature and altS to reset the scale.