I don’t think I know what plot means, at least the conversation so far is indicating I don’t know what it means, and I certainly don’t want to have a definition argument. But it seems to me that most of the plotty stuff you’re mentioning Paul is always important to a good sandbox. (Also I probably don’t know what sandbox means either.) Big Events happening are, to me, important because they’re a part of the setting and make it feel dynamic. And who knows, maybe the players will begin to be more involved with them if they choose.
But I do like “sandplot”. Not to overwork the metaphor but I like the idea of stuff happening in the sandbox. Take a scoop of sand out here, surrounding sand shifts into place. Move it there and it spreads out impacting the sand around it. Neat term!