The diff is there because as you say the wheels need to go at different speeds around a corner (the outside one has to travel further). With a normal (open) diff, if you're cornering hard then what can happen is that the inside wheel is very lightly loaded due to weight transfer, so virtually all the power might end up going to that wheel since it can spin a lot faster, which means you lose the power because it doesn't get put down on the road properly.
Your question is a good one and I can see your thinking. Unfortunately I don't know the specifics of exactly how the TRC works on the IS200 to be able to comment on that. For example, does it just work front-to-back (i.e. detects if the back wheels are spinning faster than the front ones, indicating wheelspin at the rear through lack of traction), or does it work side-to-side (as in your example) too ?Perhaps someone else might know more ?