There is a rule mandating that there must be one day off a week. That day is simply an "on your own" day where team members are not required to meet together under a coach's supervision. I don't know of any program that interprets this to literally mean an athlete must not be allowed to train. Running is a sport that requires much fewer hours per day/week than other sports that spend 2 to 3 hours daily at practice. It should not be held under the same guidelines but the NCAA doesn't make any distinction between football and any other sport.
Before this rule, which came out in the late 80's I suppose it was not uncommon for teams to schedule practices every day yet I always remember running on my own on the Saturdays we didn't have a meet. We always had an organized practice on Sundays though.
I'm a firm believer in committing your athletes to train every day. A day off should be taken at appropriate times like for instance when one is ill or extremely run down. Even one day that training is very limited and may just be a 4 or 5 mile run is better that a day off. I know that all the naysayers will counter that this is wrong but I think the first step in getting young runners committed to the sport is reinforcing the idea that training is a daily lifestyle routine. Once this is accomplished, consistency becomes much easier and running becomes something that is done easily and automatically. It becomes less of a chore mentally. Maybe it crosses over into compulsive tendencies, but to stay consistent and at a level for the long time it takes for the gains of aerobic fitness to ocurr, this can be a big advantage.
I know a few examples of elite distance runners that took one day off a week for religious reasons but these were highly motivated, intelligent runners who understood how to make the most of those 6 days they did train. For the less talented, I would recommend the best path to improvement would be to train every day.
I also know that there are volumes of research probably that proves taking one day off does not detract from a training program. I just disagree, perhaps I'll eventually change my view on this. I know that the day I made up my mind that I was a runner and that running was an every day committment was the precursor to a lot less zeros turning up in my yearly runninglog.
Nearly every single running book I've ever read recommends taking a day off whenever a slight cold occurs, a possible pre-injury condition occurs, resting heartrate is up. But the one book I read and probably the only one that stresses daily running if at all possible (of course I realize that a high fever or a stress fracture is an exception) was a book by Marty Liquori on training. When people take frequent days off and they have yet to fully commit themselves and haven't acquired the confidence to be a total competitor, those people I can easily predict probably take many other days off that they could have easily trained. More importantly, I would predict that those people are less likely to make the consistent gradual progress in their workloads required to raise their fitness levels to the maximum of their ability. And they are the ones who will fall short of their potential.
That's my spiel. Let me know how off base I am because any feedback is welcome.