To use your wording; belief is a necessary component for coherency in general.
It is true that a "black" man is not bioligically inferior to a "white" man. That is not a matter of choice, even though the desicion to undertake the scientific inquiry that revealed this fact was a choice someone made at some point.
But the truth that every human should have equal rights is a matter of choice. It is true because we have combined a set of facts and other beliefs and formed a statement that we don't care to dispute. You cannot find any empirical fact to support this claim, and you cannot find any to disprove it. In such a situation, the only thing we have to go by is choice.
I am not saying that belief is less effective, merely that there is no justification for belief other than what we want the truth to be.
So, for instance, tens of thousands of children die every day from hunger and illnesses that are simple to cure with our knowledge. This is fact, and it is true.
And we, who have the power to do something about this, have chosen to believe that it is not our responsibility. That is why we name our efforts to help charity.
The choice is made over generations, within a social context, but also on an individual basis. Everything that Gandhi accomplished began with a choice he made not to accept the way things were around him. His individual choice became the choice of many, and even today people choose to embrace his beliefs and hold them for true.