I attended a no-name college and went to a top-tier university for my phd (think mit/stanford/cmu/berkeley). I also taught at a different top-tier university. Everything below is specific to CS.
I think that top-tier universities are different in the top 20% and bottom 20% of students. The top 20% because you won't find those types of people at no-name. The bottom 20% because they're at least not completely incompetent (unlike the bottom 20% at no-name).
Here's how I break it down:
Top 20% of students at top universities: They really are that good. Also, they are the ones who benefit most from the intense curriculum at top universities. So they start off really good and actually do get a force multiplier effect from the comparatively very rigorous course-work. Most of these students end up on rapid trajectories in industry or with NSF fellowships.
Average students at top universities: Most of these students would be in the top 10% of the class at a no-name college. Still quite good, but nothing special.
Bottom 20% of students at top tier universities: Really nothing special. Comparable to the average student at no-name. Contrast with the bottom 20% at no-name, many of whom couldn't fizzbuzz on their first attempt in our senior interview prep course.
So, top tier places are really characterized by their top 20% and bottom 20%. The top 20% really are quite amazing to work with. The bottom 20% are at least not incompetent.
One last note:
> Or maybe the best of these students go on to work at companies that pay 250k/yr and I just don't meet them.
Most of my students at top-tier had offers in the $150K - $250K range. So if your sample of top-tier university CS students is sampled exclusively from non-entry-level engineers who did not receive offers in the $250K range, you're almost certainly sampling from the bottom 20% of top-tier graduates.
The students are mind numbingly average. (But don't worry they will let you know what college they went to 12 years ago)
Heck if the job requires any communication, you might be better off finding someone humble or someone who needs to prove themselves.
Or maybe the best of these students go on to work at companies that pay 250k/yr and I just don't meet them.