My thought (and I could be completely wrong) is that the TD and the sugar help to heat the soap to a higher temp, which spurs the separation/streaks (provided there is enough stearic). So far I haven't gotten any of my batches to streak without TD.
I think the only way to know for sure that it doesn't also have something to do with the stearic acid is to do some experimenting on that front. But I have had some soaps that only had part of the batch have TD added and that was the only part that had the rivers in it.
I had the opposite problem. My problems with stearic were not the ones I had used TD in and I was using a cooler temp than normal. I can't experiment with it since I have homogenized palm now. I've never had a problem with streaks or crackling when I've used TD but maybe I've just been lucky. I haven't used it for a long time. This has been a really informative thread. I should plan something with TD and experiment with it.
I thought DeeAnna's post was very interesting, too. Oddly, I had just read the other day about speckled soap and wondered about giving it a try. Long story. I won't go into it.
I also think I'm totally wrong about stearic affecting the soap. I think everyone's correct about the TD. I thought about it and I vaguely recalled someone posted a pic which showed a similar effect and people said it was from TD. So, I searched and found this topic. Just follow the link and look at marghewitt's pic.
http://www.soapmakingforum.com/f11/titanium-dioxide-question-33568/index2.html#post320112