I’ve spent years running White Wolf games wherein the guy behind the DM’s screen is called the “Storyteller.” In D&D, that guy is more accurately termed the “referee.” As the DM, I’m not telling a story; I’m just facilitating the players’ efforts. But this still has many of the trappings of a “Storyteller.” The DM builds and populates the world, laying out challenges and rewards, and constructs the web of relationships and events within which the players act. It’s up to the players to determine how to interact with the DM’s world, but the way the DM designs and presents that world influences their choices… as do the rules.
The reward system of D&D encourages players to systematically destroy all potential enemies and take their stuff. This has led many a grade-school party to treat villages, towns and Little Keeps on the Borderlands as above-ground dungeons, slaughtering well-intentioned guardsmen and innocent civilians for their money, equipment and sweet XP. In more adult play, allies are often treated in the most Chaotic (and/or Evil) possible manner; their aid is accepted until they are of no more use or they fail to truckle sufficiently, at which point they’re stabbed in the back and their stuff taken.
Naturally this approach is anathema to the Tolkienesque high fantasy attitude of 2e and later editions, where the PCs are assumed to be shining heroes of virtue. But it’s interesting to note that it doesn’t even match up with the tropes of pulp swords and sorcery! With the exception of a few particularly amoral rogues like Jack Vance’s Cugel the Clever, all of the classic S&S heroes had some sort of moral code; they were ill-inclined to harm the innocent or betray those who’d done them a good turn. Certainly Conan, Fafhrd and the Gray Mouser made a habit of robbery, but only from those whose manses were sufficiently rich to make it worthwhile. Others, like Elric and Kane, indulged in banditry and reaving, but their military efforts were likewise subordinated to achieving some higher goal.
(As to the aforementioned Cugel the Clever, his picaresque tale is a morality play in which his immoral behavior always leads to his downfall. His schemes fail not through lack of talent, but rather from an excess of venality, laziness, arrogance, cowardice or treachery, and he comes away with nothing — surely not a role model for the D&D player character!)
As a sandbox DM, I see the players as the “Storytellers.” I have no idea what they’ll do, and I want them to entertain me! As such, I have an interest in what sort of story they’re going to tell. Just as they’re not obligated to play in a setting they don’t like, I’m not obligated to run them through a story that I don’t enjoy, such as the victorious adventures of a band of amoral rogues with no redeeming characteristics whatsoever who are rewarded for their total lack of moral fiber.
This is an instance where talking things out with the players is necessary but insufficient. It’s not fair to the players to block off an avenue of play that’s explicitly rewarded by the rules! No one likes mixed messages like that. So the DM should also be ready to tweak the game’s reward system to facilitate the desired style of play.
As a house rule, if the party successfully forges an alliance with a noteworthy person or creature, the DM may treat that character as “defeated” and give out their full XP value to the party. This would dovetail with the rule that you can’t get XP for a target more than once, so betraying an ally nets no additional XP. As for innocent civilians, if they pose no threat, don’t give any XP for killing them.
This isn’t quite the same as the “story award” that arrives in later editions, as you don’t need to subjectively rate the value of any situation and the players are fully aware of the XP reward system in advance. On the other hand, there’s nothing wrong with story awards if you like that sort of thing! There’s not that much difference between “you get 1000 XP for rescuing the kidnapped merchant” and “the kidnapped merchant’s family gives you a 1000 GP reward for rescuing him,” especially if you use a “carousing” rule of giving out XP for spending gold rather than earning it.
Other options are available for specific modes of play. To encourage pacifistic thievery, you might give out XP for treasure only, so that killing people yields no XP—or even an XP penalty! On the flip side, you can encourage treachery in an “evil” campaign by awarding bonus XP for betraying those who trust you. Experience points are a flexible tool. Use them however you see fit!