Yes, if the stream being mapped to is parallel, it will preserve that parallel mapping. The text was referring to the underlying streams. For example, the following is not a parallel stream even though cats and bears are both parallel.
You can contrast that with this behavior which confirms the underlying elements are still parallel:
The idea in the text is to say that taking multiple parallel streams and applying a flatMap() operation does not preserve the parallel attribute on the underlying streams. As you pointed out, it does preserve it on the top-most Stream.of(...).parallel(). We'll add a note to be clearer about this in the text next time!