Let me play the cynic on the subject of scholarships for a moment.  While the
Ivies and some of the other schools don't offer atheletic scholarships they,
like every other institution of higher learning in the country, can and do
grant financial aid to students attending their school.  Division III schools
in other sports have the same rules but they still can and do award aid money
to atheletes based on need.  I have never liked the characterization of smaller
and "more prestigious" not giving scholarships.  They may not give atheletic
scholarships but they do still provide scholarships to STUDENT atheletes.