The terminology might not be clear. At the local school, there is a morning bell that signals the doors to open, then another bell when class actually starts. When I have been in the cafeteria the kids are finishing up, and this is before the second bell has rung. 

The full price part is also funny. The material says that kids that can afford it pay full price (as set by the school). The school is given 27 cents for each of those breakfasts, though. I don't know how you get full price and a reimbursement. Maybe it is an attempt to lessen the stigma of having breakfast by encouraging other kids to join in? As you say, could be a little over-reach.