I hear this a lot. Unfortunately the science does not support the idea that sitting on a ball all day will significantly strengthen your core, but it may habitually force you into a better posture (or it may not - be careful). Functionally you'd have the same effect from sitting on a padded stool without a back.
I'm not familiar with the studies you refer to (and you don't explicitly refer to them so I can't check them) but just thought I'd note that core 'strength' could mean either muscular development or neural development of the control of those muscles.
To be clear there isn't a study done on bouncy balls that I know of (there probably is, I didn't look it up), just based on more fundamental science: in terms of physical adaptation there is pretty much no way to increase either neural or muscular development without an increasing intensity of stimulus, which balancing on a ball will not allow you to do. You will probably gain a small amount of both for the first week or two, but then, absent of increasing stress, your body will stop needing to adapt and stabilize.
