I don't think GP is lawful-good. lawful-neutral as best, potentially lawful-evil. A lawful-good character would not do nothing when facing evil, and would not chide others for acting.
The difference is the impact it will have on our society. Isolated cases of illegal actions, to support the greater good, do have their place. But praising it to the world is going to play on others' emotions, encouraging them to do the same in the future. It is a slippery slope. People will be doing it for the attention in the future, not for the greater good.
And there ARE legal actions that can be taken in these scenarios. The worldwide praise of this act will encourage people to not even look for legal alternatives. Vigilante justice will prevail, and over time that damages the greater good.