The CEOs that belong to the club (network) can draw on the resources available to that network. It is widely believed that this ability is more important than the technical skills. It used to be correct when e-mail, LinkedIn or Google were not a thing. Now this is simply a cargo cult.
That smells like rationalization to me. "No candidate outside of my personal circle of friends could possibly do this job because being in the circle is required to do the job."