SMU is the Harvard of the Dallas-Ft. Worth Metroplex.
TCU is the Yale.
UT Arlington and UNT are U. Michigan and U. Cal.
Define “prodigy”. A lot of old folks are impressed by a kid who scores a 5 on an AP test.
There will be very specific programmatic requirements for a degree in computer science at a school like Illinois. It will be one of the best educations in the area he could receive. It would be very difficult to squeeze any music hours into a typical 120-hour degree. I highly doubt that (given he was offered no aid) he would be forbidden from doing both. He was probably rightly informed that a student who wants to be competitive in a CS program at a place like UI would be best advised to avoid distraction.
Music programs are seldom open to dilettantes in college at places where Music is offered as a major - most music coursework - beyond the music appreciation coursework that will fill a general ed requirement, is only open to people who major or perhaps minor in Music or Music Ed. It isn’t high school band or choir. Music at that level is hard - its going to require more practice time than your CS courses are going to take, plus you tend to get individualized lessons - there isn’t room for “and I want to take a few music courses”…so yes, he’d likely be forbidden from doing both since unless he declares an intent to major in music, he won’t get into the music coursework. And they probably won’t allow him to double major in two unrelated and time intensive fields unless he shows incredible gifts in both. A smaller private school without a Conservatory (you can’t, for example, take much music at Lawrence in Appleton without having been accepted - via audition - to the Conservatory) will have more flexibility - since the music major program - if available - will not have enough students to fill all coursework.
That’s like saying that Olivet College is the Harvard of banjo camps.