That's almost certainly true, but interestingly, the list of elite schools does get shuffled up a bit at the grad level. Few undergrads would consider UCSD more of a prize than any Ivy, but as a graduate research program, it would be considered very elite. Berkeley arguably has more top 5 PhD programs than any other university, but again, when two high school students bump into each other in the hallway, whip out a ruler, and measure admissions packages, Harvard is definitely a longer and thicker acceptance letter than Berkeley.
I do remember an interesting flurry or articles from a study a couple of years ago suggesting it doesn't matter much where you go to college provided you major in STEM. From my limited observations and experience, I'd say that's true - I doubt a strong CS major from UCSD experiences any real disadvantage vis-a-vis more selective ivies, but an international relations major from Yale definitely has a leg up on securing those prestigious early career internships and positions.