Is the actual premed or engineering coursework at Harvard or Princeton really that much more rigorous than that at a flagship state school? I'm doubtful.

Quick answer: YES

Longer answer - in the other reply to your doubtfulness.

This is true across the entire US system, some state flagship universities curricula are so deficient that graduate level at better schools wont even consider the bachelor level diplomas from those schools as eligible unless the applicant is top n% of the graduating class, where n is a low single digit.

The admissions committee may never publish or say it directly, but for MANY state flagship universities the B.S. level maths and science courses are simply insufficient fo higher level studies at leading schools.

Thus, companies with hiring and leadership that is aware of these conditions will also simply pass over applicants with degrees from flagship state universities, much the same as they do with online diploma mill "Graduates."

My take on this situation is that as primary education outcomes worsened in the US, state universities modulated the coursework to match the readiness of incoming students in order to keep enrollment 'available' to everyone and extract revenue from the student loans system.

The "Princeton and Harvard(s)" were differently motivated, in that they never had a goal of admitting the majority of High School graduates, and thus were not required to lower levels of educational rigour to meet eroding conditions in primary education.

It truly is a sad "state" of affairs.

I'm no expert on that particular situation, but I compared my syllabi and projects from a state flagship (not Georgia Tech, Berkeley, or UIUC) with my brother's from Carnegie Mellon, and the expectations of first/second year CS majors were extremely different. Sometimes we used the same textbook but CMU covered more chapters and their projects were more involved. Some courses that typically waited until senior year at the state flagship were common to take spring sophomore year at CMU. There were a lot of courses that were numbered as undergraduate at CMU but covered content that was only covered in graduate courses at the state flagship.