Rapidly producing immune cells during exercise, then letting them (and more) die off would be a baffling response. But pumping them into the lungs (because you've been breathing hard through your mouth) and gut (for when you make up lost energy, and maybe eat some raw meat you've been hunting)? That makes a great deal of sense.
That effect is unconfirmed in humans, but it would ground our observations in an evolutionarily-sane outcome.