The design and layout of the plumbing system is completely normal and conventional. The system outlined meets all International Building Codes. The system is set up (via valving) creating loops. These loops have the botanical treatment cells within them. These loops can be completely by-passed via valving. This does not replace place conventional plumbing, the system outlined is in addition to convention plumbing.
Greywater is regulated by state and local governments and each of these entities have their own, more specific definition. For example, the state of California, in the Uniform Plumbing code defines gray water as:
Greywater is untreated waste water which has not come into contact with toilet waste. Greywater includes waste water from bathtubs, showers, bathroom wash basins, clothes washing machines, and laundry tubs, or an equivalent discharge as approved by the Administrative Authority. It does not include waste water from kitchen sinks, photo lab sinks, dishwashers, or laundry water from soiled diapers.
The use of greywater results in lower fresh water use, less strain on failing septic tanks or treatment plants, less energy and chemical use, reclamation of otherwise wasted nutrients. All of these benefits equal a savings in energy and the natural resource that is water.