As this is way more interesting than the work I'm supposed to be doing this morning I'll give it a shot at explaining what I mean.
Couple of bits of reading material, this on network analysers themselves
and this on s-parameters
but read the next paragraph before diving into them.
Ignoring that the presentation in the first link is 135 slides long ( :o), the first 4 slides explain the general purpose of a network analyser and the diagram in slide 5 shows exactly what I would like to see measured. This is normally in terms of s-parameters of which there is some explanation on slides 27~29 and in the other link. The other 127 slides are not necessary for the purposes of this discussion.
Starting with slide 5, in particular the diagram with incident, reflected and transmitted waves, what the videos are showing are the reflected waves bouncing out into the air. This can be measured with a spectrum analyser as shown in the videos but, without knowing how much power is transmitted in the first place (incident wave) or how much is coming out the other end of the mains wire (transmitted wave), there is no context and it doesn't tell me anything other than the fact that some power is lost to the air. This is the main crux to my scepticism of the videos as it comes as no shock to me that pumping relatively high frequency signals down an un
shielded cable designed to carry 50Hz results in lots of reflected waves large enough to be measured in the air with a spectrum analyser. This is also a reason why I don't like powerline adaptors.
Where a network analyser comes in is that it can measure the reflected and incident waves giving the ratio of power lost over power sent. This is the S11 parameter. The other thing that could be measured is the ratio of power received over power sent (this is the S21 parameter). It does this by sweeping frequencies into whatever is being measured and is capable of measuring the reflections back into the device itself as well as transmitted waves if the other end is also connected (it wouldn't have to be as, putting it simplistically, we are just looking at incident = transmitted + reflected so either measure would do).
The easiest way that I see this being set up is by first measuring whatever frequency the powerline device is transmitting (a spectrum analyser or network analyser could do this) and then mimicking these frequencies with a network analyser connected to some mains cable. That would give a proper measure and cynical me suggests that the ratio going through the wire would be the lions share.
I can't be arsed to watch those videos again but IIRC the frequency coming out into the air was centered at around 100HMz which will be able to transmit either significant distance (relative to higher frequencies such as 2.4 or 5GHz) or alternatively a short distance with relatively little power which is what I suspect is going on here. The fact the that video shows an inverter powering one of them down the garden is of no relevance as the mains wire ends are still both in the same room. The invertor could be in Timbuktoo and I would still expect the same result.
Of course I could still completely wrong as what I would like to see measured hasn't been yet so I'm still open to a proper proof.