There are many Ivy League coaches who read the boards, so hopefully one of them will post a more exact explanation within a day or two.
My understanding (as a current athlete) is that each school (or at least mine) has a formula they use that includes SAT, SAT II, GPA, and class rank which spits out an "academic index." Athletes have to be within a certain number of standard deviations from the average for their class (e.g. Brown class of 2010). Not sure if it applies to smaller sports, but for bigger sports like football they get "tiered" recruits, where they are allowed, say, 30 tier 1 recruits who are no more that 1 standard deviation below, 20 tier 2 recruits who are no more than 2 standard deviations below, and 10 tier 3 recruits who are no more than 1 standard deviation below. So schools with the highest average (HYP) are at a disadvantage compared to the "lesser" ivies such as Cornell or Brown. However, the admissions departments at these schools may try to ease the burden by allowing more tier 2 and tier 3 recruits.
When you verbally commit the coach sends your application to the admissions office (usually specific people within the department handle specific teams) and if they find your application to be satisfactory they send you a "likely letter" which reads "...as long as you maintain the high academic and personal standards that have characterized your application thus far you will receive an offer of admission in March." which basically means as long as you don't flunk out or commit a felony you're golden.
The final decision, however, is in the hands of the admissions department and if you asked the Ivy League coaches if they've ever had an athlete who their school denied who went on to attend a different Ivy League school you'll get 8 yes's. Even Cornell has had to deal with this.
I know a guy who got a 28 on his ACT and got into Stanford. Needless to say he was an All-American in hs.
There are definitely dumber people at the schools than the athletes, however. The 100 dumbest people at every Ivy is probably made up 100% of professor's kids and legacy kids. However, these groups also make up about 50 of the top 100 smartest kids, so they're a lot more scattered than the athletes.