I used to 'get around this' technicality by asking at the info desks at airports where there might be a power point to charge my laptop etc, even if I'd spotted some. They'd usually helpfully point out one, or say 'oh just use any you find'. That way I figured I'd be able to argue being covered if it came down to security yelling at me or worse.
I've also since seen some airports tape over power points, presumably because they don't want it to be used.
Others openly point to them, and indicate free Wi-Fi all around and so on.
One view is that you can walk in - anyone's welcome despite it being private property. They're certainly happy for you to use their power and water in the washroom, on the assumption you're a passenger as well. One could argue reasonable assumption in court if it came down to it, but it'd be interesting to see how that went.
Sleepinginairports notes that many airports have made quite the effort in deactivating outlets.
Wikipedia notes that it's common for airport lounges to have power outlets for passengers to use.
I think the difference between the Leaf incident and what you're asking is that the guy was not somewhere he could reasonably be expected to be, with no reasonable expectation of use of their facilities. Much like if you use the electricity at your friend's house, they're unlikely (I'd hope) to be able to sue you, the airport already offers you its facilities, and indeed wants to you spend time eating, dining and so on there.
Of course, until this actually goes to court, we are not lawyers, and likely cannot do much more than speculate on what would result, unfortunately.