One thing I’d like to clarify is that Sandbox Play is not the same thing as the old rec.games.frp.advocacy Simulationism (nothing to do with whatever the Forgeites mean by that term; I don’t even want to go there). The point of Simulationism, at least at the far end of the spectrum, was that the game-world really was out there chugging along with things happening and events unfolding whether or not there were any players around; the player characters were part of the simulation, and the players helped the simulation along, but from the hardcore simulationist GM’s perspective, the game-world was the end, and everything else was the means. (From the player’s perspective, they were usually about simulating “what the character would do”, and the GM was helping by providing a perfectly consistent extremely detailed environment for exploring that.)
Now, I think it’s true that a simulationist game world automatically supports Sandbox Play, but the reverse isn’t the case. What the Sandboxer is after is verisimilitude and freedom of action, not an alternate reality. It is perfectly ok, even expected that a fully Sandbox setting can have recognizably PC-oriented adventures just sitting around in it waiting for the PCs to visit that part of the world and set things in motion. That’s exactly what Sandbox computer RPGs do. The events don’t have to unfold all over the world regardless of what the PCs do, though for a GM with time to think that stuff through it can make for a rich and interesting back-story when the PCs eventually do visit that region, or the ripples from the events reach wherever they are.
It’s also OK if the PCs are sitting in place not doing much of anything for the GM to keep generating adventure hooks to see if they want to bite any. Filling up the Sandbox world with stuff for the PCs to interact with is the main part of the GM’s job, and nowhere is it written that the only way for PCs to encounter new things in the setting is to travel around. Where it gets intrusive, and where the GM who is committed to offering his players Sandbox Play would probably tread lightly or not go at all is when the PCs are repeatedly hit with things that they have to respond to–loved ones kidnapped, getting accused of murder, having their homes burned down. All of these can make for interesting situations, and suitably spaced out all of them could occur at one time or another in a Sandbox campaign, but you really want to avoid giving the players the sense that it’s pointless to make long-term plans because no matter what they do you’re going to hit them with some big disruptive event, or worse that if they attempt to do anything that isn’t capital-A Adventuring you’re going to punish them by having something bad happen. You also probably want to avoid giving them “Jessica Fletcher Syndrome”, where no matter where they go supposedly unusual things “just happen”…but that may really be an aesthetic preference on my part unrelated to Sandboxy-ness.
The point, to me, of the Sandbox is to maximize the freedom of choice of the players as to where to go and what to do, but the setting is still there to entertain the players. If it comes to a choice between fun for the players or the internal consistency and integrity of the setting, consistency and integrity take the hit. On the other hand, in many cases consistency and integrity of the setting are aids in maximizing the players’ freedom of choice. Maximizing freedom of choice means that not only should the players be presented with choices beyond “Rescue the kitten/Eat the kitten”, but also minimizing the places in my GM notes that say “regardless of whether the PCs beat the footpads, capture them, are captured by them, or run off they will arrive at the bridge just before the wicked uncle’s minions are ready to blow it up.” That’s where it really helps me as a GM to conceive of an adventure as containing antagonists who have Plans that they’re trying to carry out, but that perforce have to adapt to circumstances, rather than conceiving an adventure as a Plot, meaning a storyline with key scenes that will occur leading up to a particular climactic scene/battle. I’m sure that you can run a Sandbox-style game the latter way, since that’s pretty much the only way a CRPG can do it, but this is an area where I think that a human GM can do a better job by adopting a different approach.