Here's an interesting supposition by the Wizard. He points out that Boyd and Hall were Oswald's usual escorts at the PD, taking him from place to place. But, on the Sunday morning, Leavelle and Graves took over that task- for whatever reason. But, that freed up Boyd and Hall for another assignment- to take care of Bookhout after the shooting.
And of course, Bookhout wound up back in circulation as himself.