There was a great deal of bad blood on all sides as the 3 split - as DArnold said, Gen. Choi is dead, and no matter what others say, there is no way to really know what he wanted, because the documents left behind are contradictory and therefore inconclusive. While I personally lean toward GM Choi, for reasons I don't really want to enumerate here because of the problems such discussion has historically caused, dwelling on the reasons why and the "true" ITF - whatever you mean by "true" - will only serve to keep alive the negative feelings that occurred during the splits.
While I wish WMKS Shogun's solution would work, I find it to be unlikely in the short term, at least, because of the nature of the splits, how they happened, and the negative feelings thus caused - to work together, people from each group would have to put aside those feelings, at least to the extent that they could work together, and I don't see that happening at the moment, because there are too many people who were personally involved, and personally hurt by the events leading to the splits. In another generation of TKDers or two, working together may well be more possible - and I hope it is - and I will be very happily surprised that if it happens sooner... but I'm not going to worry about it right now - I'm just going to practice the best I can, and keep teaching my students the best I can, because in the long run, that's the most important part.