That is VERY interesting! I'm not a physio but have a long history of chronic back/SI pain. Every physio I've been to has recommended core stability exercises and pilates - but I found this just made my pain worse.
Then I went to an Alexander Technique instructor who was very much against this 'holding' and tightening of core muscles - it is all about letting go of muscle tension in the body. So with my AT instructor's help, I've learned to relax the muscles, so my posture is much better and my pain is now much less than it was.
I can see now that in my case, the muscles around my pelvis and lower back were permanently tight and I was being encouraged to tighten those muscles further through core stability exercises. So its not surprising it caused me more pain! I think part of the problem is that when all the muscles around your pelvis and lower back have seized up, its impossible to isolate the transversus abdominus so everything just keeps getting tighter. I think you have to be able to relax all your muscles before you can start isolating individual ones to strengthen.
So now I've learned to let go of the muscle tension, I have gone back to doing some core stability exercises - but I only 'tighten' muscles as I'm doing the exercises and I make sure that the rest of the time, I let it all hang out (so to speak!). I remember a physio telling me I should be contracting the core muscles ALL THE TIME, not just during the exercises - I don't have a medical background, but that never seemed right to me!
So I'm sure core stability does have a place to play in some back pain conditions, but I don't think it can be seen as the magic cure for all problems.