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(and btw, even today, while having any degree is better than none, the second round of sifting through resumes differentiates between a degree from a good school and a degree from an unknown school).

Sadly, no, not always.
In my experiences the 2nd round of sifting doesn't look at the degree at all, it comes down to how well they interview.

I got stuck with absolutely worthless team members more than once because they interviewed well with the boss but had no practical skills (or in one case because the boss wanted a statistician because it sounded cool despite having no idea what to do with one or wanting anything more complicated from them than any intermediate statistics course provided).
It wasn't until they my team do it's own counter-interview of people that our management realized they're not qualified to determine who is or isn't a technical match for the work we do, because they don't do it or know it, they just manage the people and projects and timelines, and you can't judge technical skill off people oriented interviews, because, shock here, nerds and geeks don't often interview well or have good people skills, but can be incredibly competent regardless.

It was even worse when HR was doing it, because they literally only looked at what was on paper and had even less understanding about the actual jobs they were trying to fill.