For me, exercise has been so important in my health and POIS I've turned it into my profession (I'm a personal trainer). While I can't say that I'm sure exercise reduces my recovery right after POIS, it ABSOLUTELY helps me with the nagging long term effects like brain fog and low energy.
If I cycle/swim/run at a high intensity intervals for long periods of time, the effect is best. It really does fit well with the vagal nerve tone theory, with perhaps the parasympathetic nervous system (PNS) becoming less overactive and allowing the body to be in a more "awake" state.