Hmmm, great question! The question I would ask is will running aid recovery or not? I'd also ask will it help with psychological (as important as physical IMO) recovery or not. My approach (other's might have something that works for them) is to spin lightly on recovery days and then train harder on days I train.
I think we're always trading off fitness and freshness but most of the coaching that I've recieved encourages more/not less recovery so you can go harder when you are supposed to.
gene r