Current estimates place it around 20% of the population. Wouldn't take a whole lot of sampling error in admissions to result in 40% of admitted students

Stanford doesn't try to admit a random sample of the population, and its quite posssible the things it does select on positively correlate with the conditions at issue; it's quite plausible nonsampling error (systemic bias) is a bigger issue than sampling error in explaining any prevalence difference from the general population here.