You are right he made a mistake there.
This is probably one of many typos in this preprint of Mark Spong. You should rather turn to other good books, such as the mathematically more elegant book of Richard Murray,Zexiang Li and Sankar Sastry, A Mathematical Introduction to Robotics Manipulation (MLS94). The mathematics they use is consistent in other of their books such as Yi Ma, etal An Invitation to 3D-Vision. screw theory and Lie group theory instead of Denavit and Hartenberg's minimal approach are used in the book. It is much more superior than the D-H approach, and is widely adopted in the academia (the industry is another story).
Finally, a bonus is that the book MLS94 is completely free to download (under an agreement with the publisher CRC press). It also did a terrific job in systematic treatment from kinematics to dynamics to control.
I shamelessly refer to one of our not-so-recent publication on robot kinematics calibration, in which you may find additional information on how one may switch between screw representation and DH parametrization of joint axes. The point is, one can easily deal with parametrization singularity of DH parameters if he/she looks at the problem from a geometric (differential geometry of Lie groups) aspect.