Mid-day Thursday, Bloomberg TV spent nearly five minutes speculating on Elon Musk’s flight plans for Sun Valley. The Tesla, SpaceX and maybe-but-probably-not soon-to-be Twitter chief, who is scheduled to speak at Allen & Company’s annual confab here on Saturday, still had yet to arrive at a weeklong summit that most executives attend more or less from start to finish. Musk would arrive later that evening, but the uncertainty surrounding his plans had become a preoccupation for media outside the conference, as well as an amusing sidebar for executives inside the Lodge. This was understandable: Musk, intriguingly idiosyncratic—even by the standards of the Sun Valley set—was effectively the week’s headliner, occupying the close-of-conference slot usually reserved for a Warren Buffett or Bill Gates.