Damned is this industry, when even _you_ say you have to show that "remoteness works".
I also measure meetings (counts, lengths, and mostly meeting minutes/outine jotted down by myself) and keep track of other metrics, exactly for this reason. However, I also don't happen to have written best selling books and stuff, so I really must do this, and you really shouldn't have to :-)
I have more respect for him because he chose to do this. It’s probably clear that he doesn’t have to, at all. But he’s choosing not to rely on his (somewhat) tech celebrity status and deliver on measurable outcomes.