I did a bit more looking, and it appears I was mistaken.
No, it doesn't use the main data bus of the AGP slot, but it looks like it does use the USB pins of the AGP port. I did not previously know that AGP even had USB signals on it, but according to the pin diagram, it does... A4 and B4. Weird. The rest of the connections through the AGP slot seem just to be going to ground.
So, best I can tell with that new bit of knowledge is, two of the USB ports are driven from the motherboard's USB header and the third is run through the AGP slot. The rest of the AGP fingers are just there to prevent ground loops or whatever, and all the power actually comes from the Molex. That makes a bit more sense, but it still strikes me as quite Rube Goldberg-esque.