Why does Martin Luther King writing believe the Negro people were
“victim of a broken promise”?

yes

explanation:

the ss was the main organization responsible for the genocidal murder of around six million people of european ethnic minorities, essentially jews, in the holocaust. the members of all its branches committed war crimes and crimes against humanity during the second world war (1939-1945). likewise, the ss were involved in commercial enterprises and exploited the inmates of the concentration camps as slave laborers.

the tortures and assassinations committed by the ss were the result of an ideology developed long before the armed conflict, this ideology was based on the racial supremacy of the germans over the rest.