In the D&D universe, Good and Evil are clearly cut, defined, and enforced. There isn't any gray area in D&D, in terms of morality/philosophical ramifications, nor should their be. There is no need to justify any act. It is Good, Evil, Lawful, Chaotic, or Neutral, or a combination of Law/Chaos/Neutrality and Good/Evil/Neutrality. It is never Good AND Evil, it is never Lawful AND Chaotic.
To the Good people of the D&D universe, Trolls have no rights. They eat children, they steal sheep, they ambush the helpless. They are the equivalent of venomous spiders in the real world. You stomp them to death and hope you don't get bitten when you do it.
You don't pull it's legs off (the spider equivalent of beating a troll into unconciousness) and then ask if it's going to bite you or not.
It is never Evil to kill any one of the "usually" or "always" Evil beings. One of the core tenants of the D&D universe is the battle between Good and Evil.
Could you imagine Aragorn beating an Uruk-hai into submission and then asking it nicely if it was there to kill him?
No.
Okay, first: The first D&D universe was Arneson's Blackmoore. That did not have clear cut good and evil. Read the City of the Gods. The second universe was Greyhawk, Gygax's creation a few months later. Gygax was infamous about ambiguous alignments, as seen in the Temple of Elemental Evil and the good prince turned vampire. Players are not punished, but the murdering of the good prince is known as an ignorant evil act.
Now, you started to talk about a Forgotten Realms god, which is like the fifth setting. Eberron and Planescape are terribly ambiguous and are "part of the D&D world". Hell, Planescape is a part of the Forgotten Realms world, as seen by the Great Modron March.
D&D is anything but clear cut. Every game is different and there is no right way to play Good and Evil.
To steal a quote from Planescape.
"It all depends on where you stand."
Not going to argue "What Aragorn would do", but I agree he would kill the Urak'hai. That doesn't necessarily Aragorn is an avatar of Law and Righteousness. He's a hero, yes, and he's a Lawful Good character, but he can also be selfish and human. His choices weren't always Lawful Good. That's one thing I do find odd about arguments about Paladins: Do Paladins have to be blank expressioned, unfeeling instruments of law. I mean, I read in a third edition book that a Paladin finds two demons loving one another (Think it was a succubus and an inccubus). The book raised the conflict that the Paladin must choose to kill the demons (which are usually irredeemable) or respect their love. That confused me, since I thought that Paladins should destroy Demons on sight, but the book lead me to believe that there are other tenants for Paladins other than "DESTROY ALL EVIL" (or what appears to be evil, in this case).
They used detect evil, didn't find a trace of evil on it. This must mean he either had a magical item or effect on him (Which a detect magic might have been good to check for) or he wasn't evil. Trolls are generally evil in D&D, but that doesn't mean this one was evil, especially in someone else's game. It doesn't matter if all trolls are evil in your game or most games, the players have more evidence than not that the troll is neutral or good and as a show of thanks for aiding them, they kill this troll. We don't know if the troll was actually good or neutral or even evil, but a generalization is still wrong and to carry out a sentence without even questing thing is more akin to chaos than law.
Injustice somewhere is injustice everywhere; that troll did not receive justice, which is a tenant for Paladinhood, especially for Tyr "The Even-Handed".
Good and Evil will forever be philosophized and I've seen more arguments break out on Alignment than anything else. D&D is very vague and every setting presents a different view on what it is. I don't even bother with the in-game system of alignment and go with something more along the lines of world views (such as a political system--communist, republican, democratic, socialist etc.) as that's easier to handle).
Anyway, this argument has gone on long enough. I've seen your opinions and I understand where you are coming from, but I politely disagree. I think that is fringe logic and I see you have your opinions and I have mine. I wish many happy D&D games to everyone. xD
EDIT: Page 7 of the Book of Exalted Deeds. Mercy and onward. That is the clear cut definition of Good if I ever saw one.