Racism is much more complex and pervasive than a couple of rednecks waving a Confederate flag. Toward the end of his life, King (like Malcolm X) began emphasizing the larger issues through which racism is threaded (militarism--e.g. the Vietnam War; economic inequality--e.g. the sanitation workers' strike; sexism). This is why King said that the white moderates were more dangerous than Bull Connor. The defenders of the system are intent on denying systemic racism because anyone aware of the systemic nature of racism will inevitably see that the overall system itself is corrupt.