Hi Dan,
The answer to your question depends on how seriously you take the definition of "natural" homes. The easiest way to mitigate radon for new construction is to place a plastic (usually polyethylene) sheet under all the layers of the floor. Personally, I would do this for both the radon mitigation and to prevent rising dampness (the number one killer of buildings). To me, the benefits derived from using one plastic sheet under a building are worth the impact of that material. If someone wanted to avoid virgin plastics, old garbage bags, lumber tarps and other "waste" plastic sheeting could be used.
One easy way to mitigate radon include raising the building off the ground. If there is even 12" of air space under the building, any radon will be dispersed without entering the building.
For grade based buildings where plastic sheeting is an absolute no-no, having a base layer of largish (3/4" - 2") stone that breathes to the edges of the foundation will help a lot. Embedding perforated pipe in the stone that exits the sides of the foundation will help more.
The first step for anybody to take would be to check and see if radon gas is a problem in the area of the building. Building departments, environment ministries, conservation authorities... these types of agencies
should know if radon is problematic in the general area. If it is, it's probably worth getting testing done to determine how seriously you should try to handle mitigation.
Hope this helps!