NCAA doesn't give out scholarships, the schools do. It doesn't come out of their pockets, it comes out of the school's pocket. NCAA is the biggest hypocrites of them all, they say "nobody else can make money off of these players except us!" Everyone knows that they make millions upon millions off of collegiate athletes.
Not to mention, most players have to pay their way through college. Also, most Division III schools don't allow full scholarships to be given, and who knows why. They have rules that make absolutely no sense.