That I'm not so sure. The Army paid my tuition bill. That means whatever the school would have charged me, the Army paid for. Because the scholarship money isn't included in the bill, the Army pays the full tuition and fees. The school then refunds me the amount the Army overpaid (which is the scholarship money).
So, I guess it really comes down to whether or not your school will bill the military the full amount, or the amount less your scholarship money. If it really is a merit-based scholarship I can't see why your situation would be any different than mine.