Hi.
You are right about strengthening the stabilisers. However, most patients are progressed to advanced stages too quickly.
One of the things addressed in the specific study that O'Sullivan did was ensure effective isolation of the TA and Multifidus before integration into functional movements and activities.
Using global muscles strategies (all the other abdominal muscles apart from TA, erector spinae, lats, gluts, hams, etc) are inappropriate if isolation cannot be achieved.
This includes Swiss balls. I know people who have come to see me after being given Swiss ball exercises who cannot even stand on one leg properly yet are doing high load exercises - they are fine when doing weights in the gym or hard Swiss ball exercises but stand them against a wall and lift one leg up and they struggle to do so.
With the research that is out there concerning core stability training, the weight of it tends towards isolation before integration into functional activities.
For a good summary on this topic,
www.back-exercises.com has a nice summary about progressions of exercises.
Thanks