I need to read through it more, but as I understand it, there are two polarities, and each of the 32 transponders is on one of those polarities. Each channel is on one of the transponders. When you request a channel on transponder 23, the receiver tells the LNB on the dish to switch to the corresponding polarity. All the signals from that transponder come to the dish at once, and the receiver pulls out the one it wants.
So the multi-switch tells each LNB to take one polarity and stay there, so all the channels are coming into the multi-switch at once (half on one LNB, half on the other). Then you plug each receiver into the other side of the multi-switch, and it connects the receiver to the LNB that corresponds with whatever polarity is needed. If you're like me, a big light bulb just lit up in your head as you exclaimed, "a-ha!"
A pretty neat solution for the problem. And in theory you could hook up as many receivers as you wanted to for one dish, I suppose.