I would take this as a means to interpret what the author intended when writing the rest of the book. For example, if you play in a rock band and the band leader says a new piece you'll be learning is in D minor, there's no reason to assume that the piece is strictly functional harmony with no modal content. It could be in Dorian or Phrygian for all your band leader cares. It starts with a D minor chord and stays in that area for the whole song. It's all terminology. Changing what a piece of terminology means doesn't change how you expect the music to behave. So in this case, as reading through the rest of this text, just keep in mind that the author uses minor and modal terminology exclusively for specific contexts.
In common practice music, song in minor keys tended to use a major V chord rather than a minor v chord that the natural minor scale would harmonize to. V-i has a much more resolute feel than a v-i. That leading tone gives us an authentic cadence, which was the popular sound and is still one of the most powerful progressions in music. In A minor, that would be E-G#-B to A-C-E. The G# is altered from the natural minor harmony to give the E chord that leading tone. That's the harmonic portion. Only the seventh is raised for harmonic material. As for the melodic material, when melodies were written over this sort of progression, it was found that the interval between the minor sixth and the leading tone was too dissonant. It was, in fact, an augmented second. To correct this, the minor sixth was raised to a major sixth and the interval was much more pleasant. Typically, this melodic minor scale only has the sixth and seventh raised when ascending. Descending lines would use the natural minor.
So again, discrepancies in terminology are rampant in music because of mixed traditions, reusing terminology to mean different things, and lack of standardization. I don't know anyone who would lash out at you for calling a piece minor even though it uses modal melody and doesn't always contain a leading tone of the V chord. If the meaning gets across, that's what's important. This author knows what he means and makes it explicit, although he certainly seems to think that this meaning is more absolute than I'd agree with.