This might help people sleep at night, but it's incorrect. Managers have more pay, more direct reports and more responsibility. It's the definition of a promotion.
There are upper technical people who don't have direct reports, but have more pay and responsibility. However there are a lot more in management than those positions in most companies.
I am an IC and I outlevel my manager and probably make more than my skip who is at the same level (I have some significant extra performance bonus equity grants), so no.
Obviously managers have more direct reports, the definition of an IC is that they have zero direct reports, besides maybe a temporary intern.
At any competent tech company, moving to management results in no immediate change to compensation. It is a transition, not a promotion.
At a seed-stage startup I was paid more than the CEO, and technical founder. High-value IC's absolutely can be paid more. I had plenty of responsibility, but it was in the systems not people.