Changes when \$V_{be}\$ is increased in npn transistor
The statement of the book is correct. When you increase the base-emitter junction voltage the electron current injected into the base (and thus the collector current) increases but also the hole current injected from the base into the emitter increases similar to an isolated pn-junction. This hole current is usually the dominant cause for the base current flowing into the base. Thus the collector current and the base current increase proportionally to each other when you increase the base emitter-voltage.