School prestige is an interesting concept that prospective students tend to place excessive value on (we've all done it at some point).
The effect of school prestige is usually small at best and varies by industry and the person doing the recruiting. It does seem to matter less in CompSci/IT fields to most CIOs when looking to hire recent graduates, where internship experience and technical, demonstrable skills are generally more important. Admittedly, it is true that for some specific industries (especially investment banking), most top firms won't even consider you if you didn't go to a top-ranked school. In general, students value prestige more highly than employers. More important for getting employed are your skills, your personality and ability to work with others, networking with peers and recruiters, etc.
Obviously you should try to get into the best school you can, but one that is also a good fit for you. There are so many factors that go into finding a school that you will like and prestige is worthless if you hate it there. If your reason for going to college is solely so you can go to a "top" school, you are going for the wrong reasons. You can use any university for "social mobility" if you love it enough to work hard and make yourself stand out.
(As an aside, prestige does seem to matter more if you intend to go into graduate school for a future career in academia, and even then, who and what matters more than where. You will not finish a graduate program if you hate your advisor or your research topic, and a famous professor isn't necessarily a good advisor. I am not a graduate student, but I still recommend
this blog post by well-known University of Utah CS professor Matt Might. I found much of his advice helpful.)
The idea that "HYP is all that matters" when it comes to Ivy-level prestige is, quite frankly, insulting. You are almost certainly not going to be condemned to life at McDonald's because you wanted to go to Cornell or Columbia instead. It is true that the association stems merely from the athletic division holding them together, but the connotation of each school being academically excellent is not without merit, and you would be deluding yourself to think that reputation was earned because of HYP alone.
tl;dr Prestige is overrated, go somewhere that is a good fit for you. College will do you no good if you hate your school.