Well, does it matter that jo kus modified "fullness of truth" with the relative clause "that God has revealed to man."?
And anyway, why not? A church might not be able to provide an empirical proof of that claim but what is the a priori argument against it? Why couldn't my favorite church, the two-seed-in-the-spirit, foot-washin', poison-drinkin', snake-handlin', baptized by fire holiness Church of Hungrytown (really, there's a little cluster of houses near here which rejoices in the name of Hungrytown) have the fullness of truth in a way and/or to a degree that no other community had it?
Well, at least someone noticed... :}
Regards