Yes, there IS a slight error in the rational.

If you consider the phase constellation, a constant envelope implementation
of PSK will require more bandwidth. The paths from one constellation point
to another are more direct with the classical non-constant envelope
approaches. To keep the envelope constant, the constellation trajectory
must stay on the unit circle (and sometimes even pass thru other possible
symbol states). Since the constellation trajectory must go a larger
distance in the same period of time (gotta get there in one symbol period!),
more bandwidth is required. Things have gotta be able to happen faster in
the I and Q channels.

Dan