We have renounced the shameful things that one hides; we refuse to practice cunning or to falsify God's word; but by the open statement of the truth we commend ourselves to the conscience of everyone in the sight of God (2 Cor 4.2).
Paul here as elsewhere insists on the sincerity and honesty of the apostles in the preaching of their message. They don't make efforts to trick people, they don't lie, they don't try to hide who they are, but instead they offer themselves for evaluation as they evangelize.
It seems to me that at the end of the day, when we are confronted with the gospel message we must make a choice: either believe what the apostles and their tradition tell us about Jesus, or else we call them deluded -- or worse, liars -- and go on with our day. But the difficulty of the latter choice is obvious: they are persons who have offered themselves to judgment, persecution, rejection, and ultimately martyrdom and death for no apparent earthly gain whatsoever. Where do we get the right the refuse and reject them -- a choice made in the case of many from a position of social privilege and comfort, a choice that for some costs them nothing at all and is actually socially expected?
More than that, the apostles of all people were in the right position to make a judgment as to the truth of their claims. This is not true of everyone who dies for some religious cause -- suicide bombers or whoever. The apostles are the ones who claim to have seen the risen Jesus Christ, or more properly said, to whom they claimed Christ appeared and showed himself. They were the ones in a position to know if they were right or wrong about the whole thing. And in spite of death, of rejection, or persecution, of anathemas, of excommunication, they persisted in preaching the good news. There is a point where doubting a person's sincerity, and along with it their proposals, is no longer appropriate. There comes a time when you ought to believe a person, and to refuse to believe becomes perverse.
The difficulty, of course, comes in when the choice of belief requires major sacrifices on our part. If the apostles are right, then everything about my life has to change. If the apostles are right, then I've got to give myself over to this Jesus and I can't leave anything for myself. If the apostles are right, I can't continue to think of myself as the center of my universe any longer.