That is the litmus test. JW's, Mormons, and the Popes all claim there is no salvation outside of their organization-priesthood-Ark, etc. All bible-cults claim something similar to this. It is belief in this claim that damns them, because their association becomes an idol in that the group itself becomes a sharer in the salvation event....something God would NEVER share.
I can only speak for the "Mormons," of course, but as stated above you claim that we teach that there is no salvation outside of our organization, or church. This is not true. Sects that teach divine excusivitity almost universally condemn everyone who's not a member of their church to hell. Because of the Atonement, however, all men will be resurrected and delivered from the fall. We also believe that hell, while real, is remedial and that men are not condemned because of their beliefs, but because of their actions.
So what is the role of the church? In our view, it is to provide the divine authority to act in God's name. People say that works don't save, and that's absolutely correct. At the same time, it is impossible to gain Eternal Life without works. This may sound contradictory, but it isn't. It isn't works like baptism, confirmation and the gift of the Holy Spirit that do the saving, for works don't save. Obedience to God's commandments save, and He has commanded baptism and the gift of the Holy Spirit to be administered at the hands of his authorized servants, called and commissioned by Jesus Christ. So if man is to be saved, he is to have faith, baptism and the gift of the Holy Spirit conferred by the laying on of hands. He cannot be saved by faith alone, nor by works alone.
Those who do not repent of their own sins must suffer for them, even as Christ suffered: "Which suffering caused myself, even God, the greatest of all, to tremble because of pain and to bleed at every pore, and to suffer in both body and spirit--and would that I might not drink the bitter cup...." Eventually, after the final judgment, every knee shall bend and every tongue confess that Jesus is the Christ.