From what I understand of the Walstad tank, the point is not a self sustaining tank that doesn't require water changes. IMO her main idea was relying upon soil and plants for biological filtration instead of the bacteria which we normally rely upon. Water changes would still be necessary. The point is that fish waste, when properly balanced with the amount of plant life, would provide the neceseary fertilizer for the plants. The plants in turn, use the broken down fish waste, as well as ammonia. This is fairly similar to a planted tank, except for 2 reasons IMO. One being that most people do not consider a balance when creating a planted tank, and rely on bacterial biological filtration for excess fish waste. The second being the soil is a key component in breaking down fish waste. The bacteria along with the soil would act just as the ones in lakes do. Thus when fish waste is balanced, these soil bacteria break down waste and organic matter into components which the plants can use, and no fertilizer is necessary. While water changes might still be necessary, it provides a less hands on experience than a regular planted tank, since no CO2 or fertilizer needs to be dosed.
That's my take on the Walstad method. There may still be mechanical filtration, aeration, and water changes, but less emphasis on bacterial filtration and fertilization of plants. Basically an attempt to replicate a lake in a small scale. Lakes have water movement, but instead of gravel and filters, rely on dirt and plants.
--Adeeb