When I ran a RP LS, the events that got planned out OOC'ly were done so in order to make sure all the players would be available at a certain time. This was usually the case for players who were moving their story arc along. WIth forum RP, it's a lot easier, as you can wait over the period of days for everyone (who is needed) to particpate in the thread. In-game, the RP is done right then and there, so there has to be some sort of planning for a huge event like that.
For everyday RP, it usually went about as organically as you are referring to. Our characters would just start up RP here or there in a natural way.