It's pretty easy to see the consequences of rest just prior to an event. All you need to do is study how rapidly plasma volume is lost in a highly trained athlete during rest. There are several studies that demonstrate this. In one study, runners lost a kilogram of plasma after just 48 hours of rest. Plasma volume relates directly to aerobic capacity, and their performance numbers dropped accordingly. Plasma volume goes away quickly, and it comes back quickly (thankfully). It's controlled by Anti-Diuretic Hormome (ADH), which is produced during exercise.
Also note that in the Tour de France, none of the cyclists actually rests on "rest days". A rider is sure to go out and ride to maintain his plasma volume. He may not know why he does it, but he probably knows that he'll suffer on the next race day if he doesn't do it.