Something like that.

Another possibility is that Latra was also ta'veren. That might explain how, in a society that seemingly understood the purpose of ta'veren better, the Aes Sedai split their allegiance between two leaders, when one at least (though it's not confirmed) must have been strongly ta'veren. Ta'veren are supposed to pull threads they need toward themselves. Perhaps they can also repell threads and force them to be in opposition, but we haven't seen much of that in the series. Well, perhaps with Perrin and the Whitecloaks, but that may not be what it is. Others like Elaida, Fain, Niall and so on all opposed Rand far from his ta'veren influence.

Jordan was asked if Hawkwing telling LTT they fought each other as many times as they were on the same side in TGH meant the Dragon (or Hawkwing) had served the Shadow before. He answered that rather sometimes the Wheel needed ta'veren to stand in opposition to one another to achieve a specific purpose. He never gave an example, and I've wondered if he had in mind something specific that for some reason he considered RAFO. Latra and Lews being a case of ta'veren in opposition, performing apparently conflicting but in truth complementary action so the Pattern is saved the way it should could be what he had in mind.