Okay, stupid question. But scholarships don't really cost the U any tangible $$, do they? Just on paper, right?. Sure, you can say the scholarship is worth $xx,xxx.xx, - and it is to the student; the diploma they receive is in fact worth that much $$. But from the U's perspective isn't the scholarship simply letting a student sit at a desk which would otherwise be empty?
My dad was friends with someone who owned a country club. He let my family use the facilities free of charge. It was a great deal for us - and worth about $8,000/year from our perspective. But it didn't actually cost him anything because we wouldn't be going to the CC otherwise.
Edit: @kreed5120 hit on this while I was typing.