BSP and the view frustum

I need to see which sides of a BSP I need to render. So I have a view frustum and a splitting plane. If all points of the frustum are on the same side of the plane, I only render that one side. Seems simple. So I’ve ported the code here

http://www.magic-software.com/Source/Graphics/WmlBspNode.cpp

The only problem is that code doesn’t work. It seems at first he checks which side of the plane the camera is on (makes sense) and to see if he needs to render the other side he uses some kind of GetMaxCosSqrFrustumAngle function. I’m not sure how using that lets him get away with checking only one number, or it’s specific purpose?

My intuitive idea is to check the intersections of the frustum planes for 6 corners, and then check the sides of all 6 corners against the splitting plane. That of course sounds like more work than his one number check, I just don’t understand why it works.