The idea that you can mask learned knowledge of a company's strategy by simply not explicitly revealing sensitive information is a difficult concept to wrap my mind around.

It is not possible to unlearn the information. If you are acting as a strategic advisor, the information has to weigh in your mind and you implicitly will end up revealing information, practically subconsciously. A simple case would be where one company explains an experiment they ran (perhaps testing a feature with a small part of their customer group) and the result of the experiment. If the competitive company comes in and says they are thinking of running a similar experiment and explicitly asks the advisors what they think—what is the response given?

I have a hard time understanding how this type of accumulated information could not enter into future judgments the advisors are making. As a management consultant who faces this type of challenge frequently (and overcomes it by avoiding competitive clients and never sharing my work) I am honestly curious how one elevates themselves above this type of subconscious thinking.