It’s the student for sure. A great student can go to a less prestigious college and do just as well (maybe trying a little harder or trying the same level), but we all know usually, there is a reason why a certain college is prestigious, and it’s not because it’s ranked high on US News. I submit even without specific rankings, certain colleges will be sought after by those who can afford the costs. And if you cannot afford the cost, you should not go there. Benz and Prius both get the job done, and Prius is better if you are a lazy person like me who doesn’t like to stop by gas stations often to fill up the gas.
But one thing that is very important to me based on my own experience is that the college be strong across the board unless you are 100% certain that you will pursue only one specific field. I switched my majors 5 or 6 times in college but the college I went to was pretty strong in many areas, so I went in thinking I should major in engineering (I had 790 in SAT math so this was not an unreasonable decision on my part), but I found I was not suitable for this field and switched to CS, Bio, Econ and finally settled on English Lit which I found I enjoyed (not loved) and in which major I found very easy for me to get As, whereas I got Cs, Ds and even Fs with disinterested effort. Therefore, one thing I will want for my kid is that the school he goes to be strong in many areas of studies, and based on this, schools that fit this requirement are usually prestigious ones, although some state flagship schools fit the bill also.
In choosing between Berkeley and Stanford, the schools which had strong programs across the board in the region where my kid probably wanted to live and work, we chose Stanford because for us (CA residents) the difference of costs between the schools did not offset what we wanted for our kid. OTOH I myself was willing and and quite receptive to - as I said many times in this forum - my kid going to University of South Carolina Honors College on big merit money as a NMF and some other merit money. But again the thing that gnawed at me was the fact that most programs at Univ of South Carolina were not as strong as those at Stanford except for Intl Business, but my kid was not sure he wanted to major in IB. He also was not sure whether he wanted to go to a graduate school. The fact is for many kids, they are not sure of what they want to major in or even go to graduate school. Therefore if you somehow get into one of those schools which have strong programs across the board - and if you can afford the cost - it makes a great deal of sense to send your kid to that school which I submit would be quite high on the prestige scale even without all the specific rankings. I realize many people have different goals, and frankly most people don’t get into certain schools so it’s no use to talk as if going to that school was a viable choice. For example, I would not talk about or waste time comparing and choosing between Harvard and UCLA, simply because my kid did not apply to Harvard and has no idea if he could have gotten in.