This is analogous to the case of a person with a bad past. As he has done something wrong in the past - we tend to believe in the worst of him and not give him a chance. We have this weird dilemma. We need to protect ourselves and as we cannot know for sure whether to trust this person or not - we do the best thing possible for our defence. We predict based on prior behaviour of the person. This is perhaps the best defence strategy and hence justified. But in being just to ourselves - we are being unjust to the other person. We do not give him a chance to make amends, to change his ways. If we continue to mistrust him there is not way that the person can reform.
There is this human side to all things as well. It is of course up to us whether we want to be humane or not. I go by the principle - do not expect from others what you do not give them yourselves. To believe in an entity which rules above all forms of reason / logic and number - the heart. I cannot say believe in the best of everyone (it takes a Buddhist to do that) but do not shut down anyone just because logic says so. If there is an attempt by the person to make amends and if he is lucky enough that we feel his conviction we should give him another chance. Perhaps being still cautious is our duty to ourselves but give another chance where we get that feeling from the inside. That is being human and I would prefer that to any increased probability of making correct choices!