Alright, that makes more sense, the trick is that the (conserved) angular momentum vector need not be parallel with the angular velocity vector, the simplest example being torque-free precession [0]. It doesn't help that most examples of non-constant angular velocity have external forces in the mix to confuse the reader.

[0] https://en.wikipedia.org/wiki/Precession#Torque-free_or_torq...