If I'm Corporate Big Wig I am not taking direction from some fresh-out or underling. I want to talk with the Partner -- a corresponding Big Wig who has "peer-level" status with me. We hash out the big-picture strategy, then the underlings do all the hard implementation work.

I parse it as you'll get the advice as coming from someone on the same level as you, not a subordinate/minion. So in theory it's level-headed, coming from a person not afraid to state things as they are, and you are covered if you act on it.

This kind of advice is hard to get for the C-suite outside their boardrooms (which may be biased).

I meant that C suite folks see McKinsey Directors as people at their level of judgement and skill who they can talk to in an open and honest manner to get advice. I’m not saying this is good/bad or right/wrong. Lots of CEOs want a consigliere with good advice who is on their side and that’s what they pay to get with a Director.

I believe it is intended to mean "strategic advice from someone perceived as a social peer", meaning a high level important executive person, not a junior analyst.

Your mistake is trying to "parse". I am sure the phrase has meaning - it, presumably, means take advice from someone with the same social status - but at any deeper level it is quite meaningless. Don't bother. It isn't worth it.