I was thinking about this phrase. When you get baptized, you belong to "Jehovah's organization". When you go out in field service, you are. representing "Jehovah's organization". When you get disfellowshipped or become an ex-JW, you leave "Jehovah's organization".
This is a very cult-like tactic. It places the organization above reproach. It creates a sense of this untouchable being that is running the organization. So if you don't like something, there is no one to appeal to because it's "Jehovah's organization". "If he wants to change the policies on child sex abuse, he will, so just keep praying."
If everything is run by the big invisible guy in the sky, then no one has to take responsibility, and members are blinded into assigning blame for their troubles onto anybody else but themselves because it's "Jehovah's organization".