No, literally they can.
https://college.harvard.edu/financial-aid/how-aid-works/types-aid
Harvard, the most stringent of the Ivy League, offers money in several areas. The easiest is need based scholarships, where "need" is defined by Harvard for that student. This will get most athletes to a 100% scholarship. Then they apply gifts and grants, of which Harvard reports that they have over 2000, and they determine who gets those grants. Many grants are specifically for athletes (which the Ivy League allows if they come from individual donors).
To be a Division I-FCS school, Ivy League programs are required to have the equivalent of 63 players on scholarship. They meet that requirement.