[1] Of course, sometimes it is. It depends on the team size and seniority, but also depends on the expertise. I'm just saying that a manager does not have to always have a higher grade than a person on his team.
Maybe start by getting rid of the silly term - "IC". What's the difference between a product, project, sales and a people manager? They all manage something.
It's people's egos and lust for power that makes this distinction.
As I see it, an IC is anyone whose main contribution is through artifacts or other actions they perform directly, and a manager is someone whose main contribution is through coordinating the actions of others. As such, I'm absolutely ok with "project manager" and "product manager" even if people don't report to them directly.
If you have a better term, do go ahead and propose it, but let's not throw out this useful term just yet.
