The reference is the book mentioned in the original post... Here is a more specific link:
More About Energy and Power [Ch. 7 of See How It Flies]
That book is to a degree an original work, not just parroting what others have written, so Vz is defined just as it is in that book. It's a definition, so it can not be wrong...
That said, I know have come across the concept elsewhere, for instance in some text relating to the Concorde, where the concept of thrust limited lowest level flying speed is actually relevant. For many aircraft in many situations Vz either does not exist (i.e. the aircraft can climb at Vs) or the margin between Vs and Vz is so small that Vz is of no practical interest. That is why the concept is rarely used.
It does, I believe, add some insight into what happens when you are unable to climb out of ground effect. That happens when the airspeed is higher than Vz in ground effect but lower than Vz out of ground effect.