And then they have to be the ones to support the whole idea of that feedback in the first place!
I think gp is saying that part of managing and evaluating managers is to get results from the manager, but also get feedback from those they manage. If you're only getting results and not going one level deeper you aren't doing a good job as a manager.
Of course the company structure / culture has to encourage that bottom up feedback (to two levels, not just one). A lot of organizations / managers consider that "going above their head" so that kind of communication really needs to be enforced / required from the next level up.
I think the idea of "they have to support that" isn't just about managers applying this to themselves, but not wanting to set the precedent elsewhere.
If you've got 4 or more layers at your company, then there are multiple layers with both superiors and reports. If layer 3 says "hey, layer 1, tell us if layer 2 is doing well", then it's pretty obvious 4 should go ask 2 the same question.
It can still happen, not everyone is opposed to feedback, but implementing something like this at any layer can get opposition from everyone anywhere in management who worries they'd get a bad review.