"You have to believe what they do, not what they say. Here are the rankings for social mobility for some selective schools:
Harvard - 186 (one of the better ones)
Princeton - 186
Brown - 224
Hopkins - 241
Stanford - 241
Yale - 285
Vanderbilt - 291
Dartmouth - 303
Chicago - 335
WUSTL - 381"
The biggest thing that tilts things towards high SES is high selectivity. We all know that the test scores, GPAs and fancy EC records screened for by highly selective schools are highly correlated with higher SES.
Because of the priority on selectivity, it is no secret that schools may often fill up some of their diversity slots with URMs from professional or international backgrounds. The Obama girls seem to be quite smart and deserving of their spots at Harvard and UMich. They are URM, but also high stat and very high SES.
In the UT/Austin affirmative action litigation, UT acknowledged that they were using their race conscious holistic admissions to admit the kids of suburban URM professionals who had good stats but who missed automatic admission under the Top 10% (really top 8%) plan.
Then you get a further tilt towards high SES by going with SCEA/ED, legacy admissions, recruited athletes, and development cases.
On the other hand, Harvard uses the dough it gets from donors and high SES parents to fund full rides for 20% of its enrolled students.