What's the benefit of delaying a tenure-track position for doing a postdoc (when you already have a tenure-track offer)?

I've seen candidates for tenure-track positions in computer science that managed to negotiate a starting date that is a year later than originally planned. During that additional year, they all seem to be doing a PostDoc in various places.

I'm wondering what the benefit of this is. Many departments provide you with a lighter teaching load during your first year, so it seems to me that the overhead with moving to a new place (for just a year), working on a postdoc salary, and then, before the 12 months are up, moving again, doesn't strike me as an efficient way to develop one's career.

Is there some big advantage of doing such a postdoc rather than immediately starting your tenure-track position that I'm missing?