Your right JCO....there are many ways to set up a system. Also your right about the 'bio' . It should be before the plants.

In your drawing ( nice drawing by the way)....there is a pump on the leaving side. That would make it a 'sump'.

Take away the pump in your drawing....turn the 90 upside down. The water can flow without being pumped.
Infact, the pipe can go all the way to the ground/floor travel across it....to the GB's. The pipe can turn up and still carry water to the height of the beds, as long as it's lower then the height of the water in the clarafier.
I believe that's how their set up is.

Here you see the exit pipe of my clarafier, comming out the side of the tank. It travels down to and across the ground. Then turns up and into the GB without being pumped. The pipe (on the ground)keeps going to another GB and to the duckweed tank.
The water level in the clarafier, is at the upper line on the outside.