I think Eric did a great video on this some time back:
http://www.youtube.com/watch?v=hLXOzQQ2ePM
I think there are 3 main counter points to the "always an organization" self-serving propaganda:
1. JW can't identify any organization from the time after the apostles to the time of C.T. Russel. If God was using an organization in Russel's day then why didn't he join that organization instead of forming his own group which was later transformed into an organization by Ratherfraud?
2. God already has a heavenly organization headed by Jesus. Jesus is fully capable of organizing and overseeing the preaching work from heaven using angels and holy spirit to direct individual christians on earth. So for the preaching work to be accomplished globally all individual christians have to do is follow the leadings of holy spirit, preaching when and where the spirit impels them. The book of Acts records accounts of angels and holy spirit directing individuals to preach in certain areas and to certain individuals. Why would it be any different today?
The JWs' saying that a visible earthly organization is needed to carry out the preaching work globally is not only redundant but is also an affront to the competence of God's heavenly organization. The claim implicitly demonstrates their lack of faith in the ability of God's heavenly organization headed by christ to organize and direct the preaching effort using only holy spirit and angels and unaided by human oversight. It reminds me of the people in Samuel's day who wanted a visible human king which Jehovah regarded as an affront to his own invisible kingship. The JWs are actually mirroring this attitude. Their reasoning demonstrates that they can't imagine Jesus using just holy spirit and angels to organize and direct the preaching effort without human oversight. It reveals that they actually lack faith in God, Jesus and his heavenly organization. They have to have a VISIBLE earthly organization run by humans because they are really walking by sight and not by faith.
Of course, it is the organization that is pushing the visible organization propaganda that the JWs are just parroting. The organization uses such propaganda to make itself relevant - as a necessity in the lives of JWs. It is a self serving idea that it feeds all JWs to make them dependent on it and so that they will continue to donate funds and labor to upkeep it. This brings me to the third point.
3. Hierarchical organizations like the JWs' ultimately violate the principle Jesus highlighted at Matthew 6:24: "No one can slave for two masters." Visible earthly organizations have to be headed by imperfect men and you know the saying 'absolute power corrupts absolutely'. So inevitably these organizations headed by imperfect, corruptible men eventually develop self-serving motives geared at serving the organization's interests or the interests of the leaders, and which clash with the christian requirement to accurately and impartially follow the teachings of the bible. For example, if it is deemed necessary to sell literature to raise money to sustain or enrich the organization then the organization might implement that policy and twist some scriptures to support it. But this position would clash with Jesus' words: "you received free, give free". A situation of two masters is thus created - Serve God by obeying the bible, or serve The Organization by selling its literature? In this way earthly organizations headed by men divide the christian's loyalty and devotion to God, putting him in much the same position as someone slaving for two masters. But it's made all the more pernicious when the christian is misled to believe that the organization is God's organization and obeying the organization is tantamount to obeying God. This is what Watchtower has done.