I figured out the problem by reinstalling the homebrew installation of PySide.
When you install using homebrew, you get a warning that
For non-homebrew python (2.x), you need to amend your PYTHONPATH like so:
export PYTHONPATH=/usr/local/lib/python2.7/site-packages:$PYTHONPATH
Ran this and the module worked.
To make the change automatic rather than having to type the line each time I opened a new terminal console, I needed to add that line to my ./bash_profile file.