It's not unusual for schools to tell a recuit he needs to get at least a certain score; it's not unusual to tell a kid who is getting an oral offer that the offer is contingent upon a certain minimum.
My best information is the Yale team has a 31 ACT average, but I doubt there are any 27s (son told me).
Arguably the best player ever to play Ivy ball over the past decade was recruited with a 28 (dad telling me). The better the kid, the more leeway; subject to the 28 min.
For Ivy players, I am under the impression that a kid must have great grades, most difficult HS curriculum offered at that school, and a consistent (extremely high) test score. Outside activities are not relevant - while for the non-hooked applicant, those are extremely important (son did HS minimum; daughter headed the HS portion of the local food bank, in addition to a HS sport). While a full completed application is required, the essays are not particularly important (son wrote mediocre uninspired essays; daughter crafted, redrafted, and redrafted hers).
The pre-reads the Ivy's do really helps.
I will opine that NO Ivy coach will hold a spot for a recruit hoping for a magic number. Recuiting is hard enough for the Ivies with each school getting 6 - 8 likely letters; therefore, futilely hoping for a magic number could reduce both the size and quality of the class. At a school which brings in 15 a year, there is no such worry.
Test scores can be the most difficult hurdle - as a poster noted, many HSs have grade inflation and uneven grading, so the scores are the apples to apples comparisons which are critical for similarly situated students. For players, attending and absorbing the test prep classes can be challenging because of travel ball; therefore, the earlier a kid's HS curriculum covers the material needed for the tests, the earlier the kid can begin testing. For Ivy League hopefuls, those AP classes are all capped with tests (and the prep associated) so between the AP testing, the multiple ACT/SAT tests (and prep), and baseball year round, looking way over the horizon (I.e., before 9th grade) really helps.