These type of scholarships have been the topic of discussion for weeks in a Financial Aid course that I'm taking right now.
There is a thought out there that colleges should try to make themselves affordable to all in some way. One way is to not offer merit based scholarships to those who can afford to pay (in essence yes, the school has a certain amount of funds to grant and if you give away funds to someone who could otherwise pay on their own, someone who couldn't pay wouldn't be able to attend, Whereas if you only award funds to those who have a financial need as well as academic merit, then the need student can attend and the full pay student can attend). Not saying that I agree with this thinking, just wanted to state what some thoughts are.
Before taking this class, I had always thought "A school with an expensive price tag doesn't need to make itself attainable to everyone. Those that can afford it will attend, those that can't will go to a school that they can afford". During this class, I have come to understand why a lot of people would think otherwise.
I have perused many college websites searching their financial aid practices for this class (and for my own DD), and I have found several schools that only offer merit scholarships to students who have a financial need. Merit scholarships without the financial need part is thought to sway a person's decisions (as in the college trying to craft a certain type of student for it's own personal gain.) One that attached a financial need to it are thought to be looking out for the best interest of students.
I seem to remember the Denzel's son case - Denzel said no and the football coach said that Morehouse wasn't offer him the scholarship, they were offering it to his son because he earned it. I thought that Denzel allowed him to accept, but also donated a considerable amount of $$$$ to the school (but I could be wrong).