The purpose of the sentence "These are the hard, brutal, and unbelievable facts" is to impress the urgent need of a radical change in the law and society's attitude related to the racial injustices being fought. It's one of the four basic steps in any nonviolent campaign: collection of the facts to determine injustices are alive (police brutality, unjust treatment of Negroes, bombings, refusal of good faith negotiation)