Yeesh, Isshinryu politics sound like they are messy!
It can be. The story I hear is that Master Shimabuku named his son-in-law as his successor to Okinawan Isshinryu, passing over his own son, who (I am told) had no interest in karate at the time. However, his family was upset, and they pressured Shimabuku-san to change his mind. Finally, old and sick, he did. However, Master Uezu considered this invalid and ignored it, continuing to believe himself the designated head of Isshinryu.
Meanwhile, years before, Master Shimabuku had trained a number of American Marines, mostly for a year or two, tops, and had awarded them all high-degree black belts when they left Okinawa, telling them that they should continue to practice and eventually they would be worthy of the high ranks he gave them. Some say that he told them NOT to call themselves by those ranks immediately - some say otherwise. In any case, several of his American students did come back to the US and opened dojos, mostly proclaiming the ranks he had given them. Earned, unearned? The founder gave them - who can say they were earned or unearned if not the founder? But some resented this very much, especially in Okinawa.
Apparently, Master Shimabuku also had a tendency to not to want to hurt anyone's feelings, so he told a number of his American (and Okinawan) students that they were his "number one" student. They each took it to heart, so we have many heads of various Isshinryu organizations proclaiming that they were Shimabuku's 'number one' student - probably all telling the truth, too, in that the founder said it!
Master Shimabuku also visited the US and toured the US dojos several times, teaching and testing and awarding dans and so on. Some say he wrote a letter rescinding all the American black belts high degrees at one time - but most Americans ignored the letter. Later visits were made by Master Shimabuku and he did not make an issue of it, nor did he refuse to recognize the belts they claimed - so what to make of that?
However, Master Uezu has also visited on a number of occasions, and he also has had little bad to say about the various dojos or American senseis he has examined. I am told he has been to my dojo, long before my time. I had the good fortune to work with him when I was stationed in Okinawa, but I did not learn karate from him, to my great detriment.
By and large, I am pleased that I happened to end up in a branch that was taught by Masters Harrill and Mitchum. Not that the others were bad or wrong, but we really do strive to do Isshinryu the way Master Shimabuku taught it. Is it right, wrong, authentic, authorized? I don't know. But it works for me. I'm mostly immune to the politics. I'm just here for the karate.