To support this statement, we can point out that the Civil Rights Movement was not led by Congress or even by any major national organization.  Instead, it arose mainly through the efforts of individuals and local groups, particularly in the years after the Brown v. Board of Education decision.

The Civil Rights Movement was driven largely by local groups and by leaders who were not (before the movement, at least) nationally famous.  A good example of this was the Montgomery Bus Boycott that started in 1955.  It was started by the actions of local people such as Rosa Parks.  It was then maintained by the efforts of hundreds of local people as well as by the leadership of Martin Luther King, Jr., who was not a national figure at that time.

This sort of story shows us that the Civil Rights Movement was a grass-roots effort.