It can mean that but to say class is the problem not race is wholesale incorrect. It suggests that a white and black person of equal class, equal education, equal job etc will always be treated equally by the police for instance, the black person will never be overlooked for employment or promotion based on race etc etc. If a white man of equal class, education etc to the black man in Central Park who politely asked that woman to put her dog on its lead had have asked that woman to put her dog on its lead would she had have called the police saying she’s being threatened by a white man or would she have said I’m being threatened by a man? Would she have even called the police at all?
Like I said, saying it’s a class issue not race a issue is a far right trope as black people aren’t equal to white in any class.