McKinsey is a conglomerate of silos, and it's entirely possible for McKinsey NY to be working on something that's related to something McKinsey Atlanta is working on - that doesn't make it a conflict of interest.
In any more than banks advise and act for all sorts of clients who have related interests.
There are reasons to maybe having Red Flags (or points of concern really) about McKinsey people but I don't think that this is generally it.
I would hire everyone from McKinsey that I know if there were a role for them, and their 'integrity' wouldn't remotely be an issue. The issue frankly is how applicable their skills would be in most operational environments.