The scholarships may be privately funded, but 84% of Stanford research funding in 2012 was received "directly or indirectly from the Federal Government". That's a quarter of the University's overall income, according to its annual report[1], before you start accounting for tax breaks. I don't doubt the government gets a return on that strings-attached investment, but welfare has positive externalities too...

[1]http://bondholder-information.stanford.edu/pdf/AR_FinancialR...