The BigBoy is not just any old fan
The Fan-Only connectors on some power supplies are designed to regulate fans in the size range from 80 to 120mm. I hadn't had this exact question before, but I will see if future revs of the manual can be made more explicit.
Those Fan-Only connectors work by regulating the voltage, and the reduced power of those plugs couldn't drive a Big Boy downhill with a tailwind. The Big Boy must be on a regular Molex for the same reason you don't want a 3-pin connector so you can hook it up to your mobo.
The reason we say to set a Tri-Cool to High if you are going to regulate it with another component like a fan controller or a Fan-Only connector on a PSU, is because the switch reduces the voltage going to the fan. If you take a low amount of voltage and then give it to a Tri-Cool that is set to Medium, the voltage gets reduced again and the fan can't spin. Only set the fan to High if you need that much cooling, or you are going to control the speed with another component.
Hope that helps!