Since they operated directly under the wires, I think this is clearly a near field.

Generating power from far fields does not seem likely to get any meaningful yield. I remember my father showing me how to build a passive radio receiver using a strong sender nearby and it worked. No other power source involved but you could listen to the (weak) output. So in theory possible, but not really useful.

The earliest radio receivers that I built as a kid were entirely passive, eg a tuned circuit and a diode, and the captured energy was enough to drive a ('crystal') earpiece. I was many many (tens/hundreds of) miles from the transmitters.

This is exactly it. If you were to do this 'at scale' you'd end up having to generate more electricity to compensate for the losses, so it's clearly theft. Whether your grid coupling uses a capacitor or an inductor isn't relevant, clearly you are taking energy from the grid and is the thing that matters.

Indeed, and thus I stand by my original point, though downvoted!

The UK Wireless Telegraphy Acts made it illegal to listen to something that you weren't meant to by fiat without need of any proof of harm AFAIK, so there could easily be random laws in various places outlawing this extraction of power that has to be made up by other generation, even if small.

You generally aren't allowed to extract even small amounts of power from the system unmetered with a wire either, without specific permission.