Actually, the big GAFAM-type companies recruit widely. For example, [This SUNY career center web site](http://www.stonybrook.edu/sb/features-corps.html) specifically mentions Google, Apple, and Facebook recruiting. [url=https://www.quora.com/Do-computer-science-majors-at-Stony-Brook-University-get-good-jobs]Here[/url] is a mention of Amazon and Microsoft recruiting at the same SUNY.
Yes, Stanford has a local advantage with smaller companies that do not travel to recruit. But so does San Jose State.