Perhaps because he is an extremely bright kid with a sky-is-the-limit academic future AND has mentioned that he especially is interested in studying medical technology, looking to a possible career in medical engineering.
And of the most prestigious programs in medical technology (U of Pennsylvania, Johns Hopkins, Case-Mellon, Washington U-St Louis...) the U of Iowa is at the top of the list of those programs which are also serious Division 1 athletic programs...and easily the top choice among Midwest schools that play big-time basketball.
The U of Iowa has the largest teaching hospital IN THE WORLD. UIHC was one of the three sites of the landmark Genome Project. It is a huge facility in cancer research. It has billions of dollars worth of patents. It has embarked on a billion-dollar plus upgrading and expansion of UIHC that will increase its staff from a current 10,000 employee level to nearly double its staffing by 2016.
Perhaps none of this will matter in the end; it may well be that the kid in so enamored of running around in short pants bouncing a ball that he wants to extend adolescence into his 30s playing in the NBA: after all, that IS the choice of hoop stars who fall short of his rare combination of brains and athletic talent---OR he may follow the path of Bill Bradley et al and try to balance both, postponing (sometimes with fatal consequences) their post-sports careers. But it certainly is plausible to postulate that even if he hopes to pursue both futures he might decide that the U of Iowa Hawkeyes in combines great preparation for both..with the added advantage of being in his backyard.
The longer he waits to make his choice, most likely that is in Iowa's favor as he concludes that it is the best-suited to his academic interests and the Hawkeyes as a BT program would give him an opportunity to play college basketball at the highest level as well.
Aren't the U of I's medical advantages as a post-graduate as opposed to an undergrad? Randle could go anywhere he wants to as an undergrad and go to Iowa as a grad student if his NBA aspirations don't pan out. I'm not sure that it's a big recruiting tool.