from the Stanford alumni magazine, Stanford President John Hennessy wrote:
"In a general way, our goal seems quite simple: we look for students who have excelled academically. In this regard, to quote the Stanford Bulletin, we envision a student body "whose abilities, intellectual interests, and personal qualities will allow them to benefit from and contribute to the University's wide range of teaching and research programs in the humanities, sciences, and engineering." Further, to paraphrase Dean Mamlet, we are obligated to search for a student body that will, as a whole, use the University in its entirety, rather than engaging some disciplines while neglecting others. Likewise, we value students with a highly developed skill in one area, as well as students with a broad academic portfolio.
There are other factors, of course, including athletics, artistic or musical talent, legacy considerations and a desire for a broadly diverse student body."
Note the need "to search for a student body that will, as a whole, use the University in its entirety, rather than engaging some disciplines while neglecting others."
So, they are not going to admit only potential engineering majors.