I'm gonna side with the OP on this one. The law says allowed breaks under 20 minutes must be paid. OP was talking about allowed breaks under 20 minutes. What possible argument can be made that they do not need to be paid?
The OP was right. By Federal law, breaks of under 20 minutes MUST be paid breaks. There is no qualifier regarding whether the breaks are allowed or not. The OP could have been disciplined up to and including termination if he had been taking unauthorized breaks, but under NO circumstances is an unpaid break of under 20 minutes legal.