This doesn't correspond to my experience. In my experience McKinsey consultants prefer not to talk to lower-level minions - on the contrary a major incentive for going into (strategy) consulting appears to be to able to deal with C-suite executives directly and not having to care about understanding any of the day-to-day business.
It usually goes like this: The CEO, a former McKinsey partner, hires McKinsey to formulate a strategy for the company: Often on a trending topic like digitalization, AI, etc. The details are usually confidential so there's no involvement of lower-level employees (maybe providing some data but without any context as to why). After a few months of utter secrecy management presents some transformation strategy.
I have yet to meet a normal employee to respect what comes from McKinsey. The average strategy consultant will look down on lowly employees and prefer to have as little interaction with them as possible.
"I have a PhD in computer science from a T1 university"
Why is the "tier" of your university important here? Not trying to offend you, but that kind of elitism is part of the reason consultants have a bad reputation. And unfortunately it is reflected in their work.