In short, which college you are coming from is not that important as long as you prove your knowledge of coding at the interview. In the interview, nobody gets threated differently just because they are from Stanford vs MIT vs University of Washington etc.
Yes, but
(1) The least prestigious university you just listed is still a state flagship, and even admission to some state flagships has become pretty competitive.
(2) Interviewing is time-consuming and therefore costly for the employer, but filtering by school is quick, so the school attended may play a role in who is brought in for an interview.
