You show a very good difference between 2 possible definitions, but say nothing about the other point.
Even if you choose the most loose definition, what's proof enough for you that even that thing exists?
In this case, I accept the Battero GPS video as evidence that they have SOMETHING, based on the fact that I think it would be easier for them to actually create this prototype-level device than it would be to fake all the data & waveforms, etc. Of course I am skeptical of their claims & conclusions, but whether the device exists or not, in this case, I accept their own video.
Depending on what's at stake, my standards of proof and whether specs are met increase towards your stated criteria:
If I was spending a nominal amount of my money on such devices, I would have a higher standard of proof that there is a reasonable chance that (a) the device is even possible and (b) the seller has demonstrated the device to a 3rd party that is clearly not a paid shill of the company.
If I was investing a significant amount of money on such devices, the standard is even higher and I would want a renowned 3rd party to independently validate the actual claims being made with their own test (and not just UL repeating a contrived test).