your thinking to hard.
the PVC pipe is lined with the tubing. he just filled the inside of all the tubing with bio-balls. the bio-balls are just bacteria farms. this is where the anoxic area is. the tubing is used to grow aerobic bacteria. so when the water exits the tube and enters the PVC pipe it is divoid of oxygen.
what you say will work fine. there is a lot of head pressure in all of the tubing so you still might need a pump. Gravity could work, but i would think you would need a pretty drastic drop to get enough force to push through all of that tubing.
did i help or hurt.
G~