@SwitchBack The Wikipedia article you provided a link for (thank you for that) doesn't mention any significant difference between US and Europe earthing systems. In both regions, earthing or grounding means to connect conductive housings of electrical appliances with a grounded potential. Main reason for this is safety: if the housing gets in contact with live voltage due to a part inside carrying live voltage getting loose or due to insulation failure, this will cause a short circuit, which will instantly interrupt power by blowing the fuse.
Theoretically, ground or earth potential should be the same on any outlet in the house. Practically, it isn't, depending on the structure of the internal wiring and the power that is taken from each outlet. The result are slight differences in ground potential between appliances. If there is an additional connection between these appliances such as an audio connection, these slight differences will result in AC flowing through the shield of the audio cable. That's what is called a "ground loop" and especially if the audio connection is unbalanced, it will cause hum noise on the audio signal.
To avoid ground loops, you have to break them at some place. But you should
never ever do that on the mains power path, because if you cut the ground wire there, appliance housings lose their grounding and in case of a fault they will carry live voltage at their outer surface, which is life-threatening.
Fortunately, it is not necessary to break ground loops on the mains power path. Instead, one can do this on the audio signal path. In the Behringer HD400 a transformer is used for this purpose. Transformers pass signals from their inputs to their outputs through a magnetic field. Thus they provide a kind of an "air gap" between the ground of the audio source (e. g. an interface's output) and the ground of the audio sink (e. g. the input of powered speakers or a power amplifier). This "air gap" breaks the ground loop without affecting the audio signal and - very important - without causing any safety hazard.
You're right when suggesting to make sure that the neutral pin of an appliance is connected to neutral of the outlet. If turning the plug by 180 degrees is possible, one can swap neutral and live pins in order to reduce hum noise. But doing so does not eliminate ground loops, because ground loops run through the ground pin, which is not swapped. So even if the swapping is done automatically, you won't get rid of ground loop noise. But at least the GND Defender makes swapping possible on plugs that are keyed in a way you can't turn them. In many european countries, however, there is no need for such a device, as plugs are keyed in a way that allows turning them by 180 degrees.