I'm not sure UIUC and UT-Austin are great examples for second-tier schools, as both are top 10 for graduate CS departments.
It's an excellent opportunity for summer research jobs and the such, but otherwise does not translate well into the lower curriculum unless you want it to.
I can't think of a top graduate program with a poor undergraduate program. And CS tends to be extremely rigorous, so I am honestly surprised that a recruiter would view a degree in CS from UTex as a non-indicator.
But I'm not trying to shoot the messenger. Perhaps UTex and Brown were selected to specifically illustrate the phenomenon here, that a highly regarded engineering school might be discounted while an Ivy league school that normally isn't associated with Computer Science would be considered a positive indicator.
It's a little hard to argue with a recruiter, they've done far more placement than I have. But I have worked (and done lots of interviews for) for a large silicon valley company, as well as for a few startups, and personally I think that a CS degree from UTex at Austin or UIUC would be very positively received.
Undergraduate curricula tends to be standardized, and nobody gets out of a top school without taking the tough courses. But you can get wiggle through an MS. But at the door... not so sure, the selection requirements (undergraduate GPA and GRE) at Berkeley were very high for any kind of admitted grad student. However, Berkeley doesn't have one of those "industrial affiliate" programs that are profit centers. However, I don't think these programs harm the universities that offer them at all - the students are almost always already employed at good companies doing interesting work, and I think the other students benefit from their presence.
However, my experience (as a holder of a degree from a further-down-the-list university) has been that after the first job (and then even moreso after the second), the name of your undergrad university matters much less. Having real, productive work experience is itself a powerful signal—so hopefully those first jobs let you do interesting or varied enough stuff to have something good for the resume. So I don't have the network (yet!) that a Stanford or MIT grad would, but I'm not landing on discard piles either.
The reason being the only people that go to private universities are the ones without good notes to earn a place at the public universities, but whose parents are rich enough to pay for the university.
People with degrees from private universities are told they bought the degree.