/diy/ - Do It Yourself

I want to make a small 120VAC to 24VDC power supply. I took apart a 5VDC 750mA wall wart usb phone charger for inspiration. The circuit seems backwards to me.
I was expecting transformer -> rectifier -> regulator. When I got the thing apart I found two boards;
One has the USB connector, couple diodes, resistors, and a capacitor.
The other board has the transformer, a transistor, a rectifier, a 6 pin controller/regulator?, and some passives.
It looks like the AC lines go directly into a rectifier. The wires to the secondary board with the USB conenctor on it come directly from the transformer.
What black magic are they doing here? Is the IC on the main board running off rectified mains? Fireing the transistor at something other than 60Hz?
The output of the transformer must be single wave rectified and smoothed with the cap. Does this just allow them to claim 750mA peak without having to drive it constantly?
Why not just send clean 5VDC directly to the secondary board?