Part of the reason we only accept 1/3 is because we have so many kids who have absolutely no business applying, but they do just because they want to go to school in Miami and assume it isn't that hard to get into because of the old "suntan U nickname". I actually knew a ton of kids who applied to Miami with like C+ GPAs, however they weren't applying to schools like Penn St. because they knew they wouldn't get in because Penn St. has been good for decades. A lot of these kids who end up going to FIU, FAU, or Barry also applied which brings up the number of applicants.
The ACT score thing is also driven up a bit by kids who got into schools like Notre Dame or UNC, but chose Miami because they figured the benefit they would get from graduating from those schools does not outweigh the fun college experience they would get at Miami. Other schools don't really get that benefit. If you get into Penn State and Notre Dame. You go to ND because it will help you get a better job.
Finally, a smaller reason, but one to factor in. I knew at least 30 kids that got into some really elite schools like Duke and even a few kids that got into IVYs, but chose Miami because their parents owned massive businesses and they were going to work for them after so their degree didn't mean much and they would rather spend 4 years balling in South Beach than 4 years ******* around in NC.