Others in the company begged to at least back it down to a count of people 2 degrees away; but the founder insisted that the magic was the 3-degree version. So instead the company pursued technical strategies to speed up the 3-degree count; don't know what those were precisely, but it seems that they were not pursued as zealously as they could be (due to VoIP, etc. distractions).
My understanding, by the way, is that the network size was computed on page-load until surprisingly very late, due to the perceived need for real-time. Even after it was cached, it was still computationally expensive, as your numbers were computed (roughly) every time your 3-degree network added a link.
In retrospect, A/B testing could have been used to test the executive vision. So although my first reaction upon hearing this story (years ago) was: "that's big-O insanity," now I think that it's just as much a story about willingness to subject vision to empirical data and performing clinical cost/benefit analysis (when appropriate).