Groups don't get free dining. We have friends who have traveled with a couple of different sporting groups and they aren't eligible to book general public discounts. They'd lose their group benefits, which are usually better, and in some cases (Pop Warner) the group's contract with Disney specifies participants have to make their travel arrangements through the group. Since the South American groups are guided-type tours I assume that the participants are similarly locked into the bookings that the tour company makes, rather than going off on their own to find the best deal.
Now with sporting groups you'll find some families that do book their own travel even if their athlete is booked as part of the group. I know a Pop Warner family who does that to get free dining for the family when it is offered in Dec - their son registers for a room with his team, while they make their arrangements on their own because free dining is more of a benefit to them than the group discount.