I don't think the GB is as powerful as they appear in print.
It is the corporate attorneys (most of whom are indeed based in the USA) who wield the most real and significant power, followed by the guys who run the corporations. If the GB wants something done but the lawyers tell them it is going to cause legal troubles the Society doesn't want, then the GB will defer to the attorneys. If the guys who run the corporations want something done to make life easier or wealthier for the Society, the GB will defer to the corporate wishes whether they agree with the idea theologically or not.
I have asked this many times but it seems nobody knows the answer (therefore I can only speculate): what is the LEGAL relationship of the GB to the WTS corporations? Is there ANY? Or does the GB exist solely at the sufferance of the Society corps?
I suspect the GB has NO LEGAL connection and it was set up that way ostensibly for their own liability protection. What it REALLY means is the GB has no authority except that which the WTS presidents, boards of directors, and attorneys grants to them.
Does a Branch overseer in Africa or east Asia have any real power to do anything? Not really, unless there is translation and printing going on there. In that case he "may" be able to influence the tone of the literature, either increasing or reducing the amount of psychological thought-reform that goes into the phrasing. But he can't just make rulings that run counter to the Borg because they'll find out sooner or later and he'll be removed. He is only who he is due to "theocratic appointment" and can easily be reassigned to latrine duty.
Now on the local level, it is fairly easy for a small body of elders in a wilderness congregation to run things however they wish and just play nice during the times the C.O. visits. So a local CoBE with a total body of elders size of 3 or fewer may wield quite A LOT of authority at the local level and act fairly autonomously from the Borg most of the time, if he wishes.